What is the integer quantum Hall effect?

And why is it so amazing?

Surprises [about physics in two dimensions] occurred in the 1980s when it became possible to study Landau levels [the quantised energy levels of electrons in a magnetic field] in Flatland. This happens when the electrons are completely constrained to move in only two dimensions. The surface within which the electrons move needs to be extremely flat and free from defects and impurities. Advances in semiconductor technology in the 1970s led to two realisations of this Flatland. Both were developed for technological reasons: the desire to have transistors in which the electrons and holes can move extremely fast. One class of device is silicon MOSFETs (Metal Oxide Semiconductor Field Effect Transistors). The second class is heterostructures, where layers of ultrapure semiconductors such as gallium arsenide are grown on top of each other, one layer of atoms at a time. In both classes of device, a fixed density of electrons (or holes) can be injected at the surface. These charge carriers can move freely in Flatland, acting like a fluid. Things get interesting when the number of charge carriers is small enough and the magnetic field is large enough that the number of charge carriers is comparable to the number of quanta of magnetic flux that pass through the system. Then, the quantum state of most of the charge carriers is one of the lowest Landau energy levels. 

To achieve this regime for the cleanest possible systems requires magnetic fields more than a hundred thousand times stronger than that of the Earth. Furthermore, the magnetic field must be spatially uniform in the region where the semiconductor system is located, stable over the time of the measurements, and the interior of the electromagnet producing the field must be large enough to contain a refrigerator that can cool the charge carriers in the system down to a few degrees above absolute zero. By 1980, all these conditions became possible. Klaus von Klitzing was able to perform measurements of the Hall resistance versus magnetic field in a special high magnetic field laboratory in Grenoble, France. The results were surprising and are shown schematically in Figure 35 below. There are four noteworthy features. 

 

Figure 35. The quantum Hall effect. The Hall resistance is shown as a function of the strength of the magnetic field and has a step-like structure. The integer n is related to the quantized energy that the charge carriers have.

First, there are distinct steps in the curve. At small magnetic fields the Hall resistance versus field is a straight line, as expected for the classical Hall effect. However, at larger fields there are plateaus in the curve.

Second, each of the plateaus is extremely flat. Von Klitzing found that the magnitude of the Hall voltage on each plateau did not vary to one part in ten million. As he varied the magnetic field, he noticed that the first seven digits on the voltmeter he was using did not change. He wondered if the voltmeter was broken and had become jammed. But it was working.

Third, the magnitude of the Hall resistance for all the plateaus has a simple relationship to fundamental physical constants. The quantum of resistance is defined as equal to h/2e^2 . When you calculate this quantity, the answer (25,812.827 ohms) is in the units of electrical resistance. The value of the Hall resistance is precisely equal to this value divided by an integer (n=1,2,3 …) which is related to the highest quantized energy (Landau level) that an electron can have at that magnetic field. That is why it is known as the integer quantum Hall effect.

Fourth, the observed value of the Hall resistance for each of the plateaus is independent of many details, including the temperature, the amount of disorder in the material, the chemical composition of system (silicon versus gallium arsenide), or whether the charge carriers are electrons or holes. [This independence is characteristic of the universality associated with emergent phenomena]. 

These four features are similar to those for the steps associated with the macroscopic quantum effects (magnetic flux in superconducting cylinders, circulation in a superfluid, Josephson effects) discussed in the previous chapter. Again, it is astonishing that a macroscopic measurement – of electrical resistance - of a macroscopic system can determine fundamental constants that are normally associated with properties of atomic systems. Just as the Josephson effect led to a new standard measure for voltage, the quantum Hall effect led to a new standard measure for electrical resistance.

Anyone familiar with building electronic circuits will have used resistors of varying values in ohms (Ω), e.g., 10 Ω or 25 kΩ. When these resistors are made, they are calibrated against some standard. For making integrated circuits with billions of transistors this standard needs to be extremely accurate. In 1990 the international standard for the ohm was changed to be that defined by the quantum Hall effect. Previously, the ohm was defined by the electrical resistance of a column of liquid mercury with constant cross-sectional area, 106.3 cm long, a mass of 14.4521 grams and a temperature 0 °C. Like the Josephson voltage standard, the quantum Hall resistance standard has the advantage of precision, portability, reliability, reproducibility, and independence of platform. 

An extract from Topology Matters, Chapter 8, Condensed Matter Physics: A Very Short Introduction.

Rudolph Marcus (1923-2026): theoretical chemical physicist

Rudolph Marcus died last week. He was 102. There is a nice obituary in The New York Times. He was best known for his theory of electron transfer, for which he was the sole recipient of the Nobel Prize in Chemistry in 1992.

Although the theory was proposed for electron transfer in a polar solvent it applies to a wide range of other systems, where two quantum states are coupled to one another and to an environment. One example is for Forster transfer of excitons between molecules, which is central to photosynthesis.

I will give a physics perspective, based on a talk I gave in Slovenia back in 2013. Slides are here.

Basically, Marcus proposed an effective Hamiltonian for two diabatic states and calculated a transition rate in a limit that is relevant to most chemical contexts.

The Hamiltonian can be viewed as the spin-boson model, in which a two-level system is coupled to a bath of harmonic oscillators. 

[The dense book by Weiss on Quantum Dissipative Systems makes the connection explicit in detail. A more accessible treatment may be chapter 16 in the book Chemical Dynamics in Condensed Phases by Nitzan.]

The Hamiltonian is 

This defines a spectral density, which is important for quantum decoherence, but not so much here, except it defines a timescale that determines the classical limit, which Marcus assumed.

This can be used to define a quantity central to Marcus' theory, the reorganisation energy.

The transition rate between the two quantum states is given by

I consider this to be one of the most important equations in chemical physics, particularly for the understanding and design of functional materials.

Aside. Much of this is equivalent to Holstein's 1959 treatment of incoherent polaron transport (see Mahan, Many-body physics).

A key experiment by John R. Miller, Lidia T. Calcaterra and Gerhard L. Closs in 1984 showed how good the theory was and how its predictions were counter-intuitive. The authors considered a family of molecules that allowed them to tune epsilon, the energy difference between the two electronic states. [On the graph below epsilon = - Delta G].

The vertical scale is the reaction rate on a logarithmic scale. It varies by four orders of magnitude.

What is surprising? As stated at the Nobel prize award ceremony:

"The quadratic equation predicts that electron transfer reactions will occur more slowly the larger the driving force of the reaction is. This phenomenon received its own name, “the inverted region.” To a chemist, the phenomenon is just as unexpected as when a skier finds himself gliding more slowly down a slope the steeper it is."

The theory implies an important design principle for functional materials: if optimising functionality means maximising the reaction rate, then tune the energy difference epsilon to equal the reorganisation energy E_R.

The theory illustrates two important aspects of emergence: effective theories and universality. Many different systems can be described by the same theory. The environment may involve many degrees of freedom and its coupling to the system is characterised by many parameters (the M_alpha above). However, only one parameter matters, the reorganisation energy.

For Australians, there is some ambivalence about the way Marcus' name is often solely associated with electron transfer theory. We often refer to it as Marcus-Hush or Hush-Marcus theory because Noel Hush did similar work around the same time. Some of the history is recounted here by Ian Rae and Jeff Reimers. There are also subtle debates about whether the electron transfer is adiabatic or non-adiabatic.

My only personal interaction with Marcus was in 2011 when I visited the chemistry department at Caltech. Marcus kindly took me to lunch at the faculty club, along with his research group. Then he was 84 years old. He kept publishing papers until he died.

What is a quasiparticle?

 An example of emergent entities in condensed matter physics are quasiparticles. The concept can be described with the following analogue. When a horse gallops through the desert it stirs up a dust cloud that travels with it. The motion of the horse cannot be separated from the accompanying dust cloud. They act as one entity. Similarly, in a system consisting of many interacting particles, when one particle moves it carries with it a “cloud” of other particles. This composite entity is referred to as a quasiparticle. It turns out to be easiest to understand the whole system of particles in terms of the quasiparticles rather than in terms of the individual particles.

Quasiparticles are composite objects. Like the constituent particles in the system, quasiparticles each have properties such as charge, mass, and spin. However, these properties of a single quasiparticle may be different from those of the individual particles of which it is constituted. An example is holes in semiconductors; the many electrons in a crystal act collectively to produce a hole (the absence of a single electron), a quasiparticle with the opposite charge to that of a single electron. A more striking example is for the fractional quantum Hall states; the charge of the quasiparticles can be a fraction of the charge on a single electron.

Different musical instruments produce distinct sounds because they are made of different materials, and they vibrate in different ways in response to different stimuli. In general, the vibrations of a medium reflect something about the medium itself. Chapter 3 discussed how in a crystal the number of distinct ways that sound can travel through a crystal reflects the symmetry and ordering of the atoms in the crystal.

When the skin on a drum is hit by a drumstick the skin vibrates at particular frequencies. Similarly, a state of matter responds to external stimuli such as light, sound or heat, by oscillating at particular frequencies. These vibrations travel through the matter as waves. The properties of these waves reflect the particular order present in the state of matter. Here is a specific example. When a neutron with a particular energy and momentum is absorbed by a ferromagnetic crystal the interaction of the magnetism of the neutron with that of the atoms in the crystal produces a collective oscillation of the magnetic state of the crystal in time and space. Known as a spin wave, this oscillation has a particular frequency and wavelength. In quantum theory, waves and particles are equivalent to one another. The energy and momentum of a particle are related to the waves’ frequency and wavelength, respectively. Particles equivalent to light waves are known as photons; particulate equivalents of sound waves are known as phonons. And similarly, the particle equivalent of a spin wave is known as a magnon. These collective excitations are quasiparticles. Whereas the particles in a system may interact strongly with one another, the quasiparticles may interact weakly with one another. This makes analysis and understanding of the relevant theories more tractable.

The quasiparticle concept is a powerful theoretical tool in condensed matter physics. It is the basis for the construction of models that enable emergent phenomena to be understood in terms of the effective interactions between components such as quasiparticles, rather than in terms of the actual constituent particles and their interactions. This approach requires profound physical insight in order to discern what the truly essential components of a system are. Lev Landau was one of the first theoretical physicists to take this approach, introducing the idea of quasiparticles in his theories of superfluidity in 4He and of liquid 3He. This approach was also central to the BCS theory of superconductivity. Phil Anderson was also a master of the approach, using intuition to propose models that were simple enough for analysis and yet complex enough to capture the essential physics associated with a particular state of matter. In 1977 he was awarded the Nobel Prize for work using this approach to understand two specific systems: magnetic atoms in metals and the motion of electrons in materials that are not crystals and are dirty in the sense of containing many impurities.

An extract from Chapter 9, "Emergence: More is Different", in Condensed Matter Physics, A Very Short Introduction

A more detailed and technical discussion is in Section 8.2 of my review article on emergence.

Tony Leggett (1938-2026): condensed matter theorist

Tony Leggett died last week. The New York Times has a nice obituary. One measure of his influence on me is that more than 20 posts on this blog feature his work. He received the Nobel Prize in 2003 for developing the theory of superfluid 3He.

In 1972, a graduate student at Cornell, Doug Osheroff, discovered a phase transition around a temperature of 2 mK in liquid 3He. In the 1960s liquid 3He was established to be a Fermi liquid that was beautifully described by Landau's theory. Osheroff and his advisors, David Lee and Robert Richardson, incorrectly identified the phase transition as arising from antiferromagnetic order in the solid phase of 3He.

However, Leggett argued that it was actually due to superfluidity that there were two distinct superfluid phases, A and B, with different order parameters. 

Lee, Osheroff, and Richardson shared the Nobel Prize in 1996 for their discovery.

Leggett was primed to make rapid progress, as in 1965 and 1966 he had written three papers about superfluidity in liquid 3He, albeit assuming s-wave pairing. Indeed, by 1975 he wrote a comprehensive review article on the two superfluid phases.

For many reasons superfluid 3He was significant for the broader field of condensed matter. BCS showed that in elemental metals, superconductivity resulted from Cooper pairing of electrons due to an attractive electron-phonon interaction.  The order parameter (Cooper pair wave function) had s-wave spin singlet symmetry.

In contrast, superfluid 3He showed that Cooper pairing could also occur in a neutral Fermi liquid, and have non-trivial symmetry, i.e., p-wave symmetry and spin triplet. The order parameter has 18 components, compared to only 2 for elemental superconductors. There is spontaneous symmetry breaking of the local gauge symmetry, and spin or orbital rotational symmetries. 

The Cooper pairing in superfluid 3He is not due to a fermion-phonon interaction but due to spin fluctuations.

The fact that Cooper pairing was possible for different symmetries and mechanisms than for elemental superconductors was significant in that it meant it was reasonable to consider this possibility for superfluidity in neutron stars, and superconductivity in cuprates, strontium ruthenate, heavy fermions, and organic charge transfer salts.

There is rich physics associated with the symmetry breaking: 18 collective modes of the order parameter, textures such as boojums, and exotic vortex cores. For vortices, there is also some (controversial) connection to cosmic strings, including experiments that test the Kibble-Zurek mechanism and the electro-weak phase transition in the early universe.

Aside: My Ph.D. thesis was on the theory of the non-linear interaction of zero sound with the order parameter collective modes in the B-phase.

Leggett's development of the theory of superfluid 3He was amazing and certainly worthy of a Nobel. However, I think he made an even greater contribution to physics through his work on the theory of macroscopic quantum effects in Josephson junctions. This work was the basis for the experimental work that was honoured with the Nobel Prize last year.

With his student Amir Caldeira, Leggett performed concrete calculations of the effects of decoherence on quantum tunnelling in Josephson junctions.

[The NY Times obituary mistakenly says this work began after Leggett moved to Urbana. It was done while he was still at Sussex].

The formalism they developed involving the spectral density is the basis for most theoretical treatments of decoherence in superconducting qubits. A relevant toy model is the spin-boson model, and in 1987 Leggett published a seminal (but rather dense) review on the subject.

Leggett aided our understanding of cuprate superconductors. He contributed to the theoretical ideas that were the basis of the phase-sensitive measurements that established the d-wave nature of the order parameter. He also showed that experiments with inconsistent with  Anderson's interlayer tunneling theory.

I recommend reading Leggett's own scientific autobiography, Matchmaking Between Condensed Matter and Quantum Foundations, and Other Stories: My Six Decades in Physics and his book, The Problems of Physics

Responding to scientific uncertainty

Science provides an impressive path to certainty in some areas, particularly in physics. However, as scientists seek to describe increasingly complex entities, moving from chemistry to biology, and then to humans and societies, the level of uncertainty increases.

One observes a wide range of responses to scientific knowledge being uncertain. Here are a few.

Denial. Science is about facts and absolute truth. There really isn’t a problem. We should just trust the scientists.

Minimisation. There is some uncertainty, but it isn’t anything to be concerned about. Some scientists will also minimise any uncertainty about their own research. This may occur because of career ambition. Others will minimise public discussion of uncertainty to try and avoid promoting the science scepticism discussed below.

Optimistic perseverance. The uncertainty is openly acknowledged. Some of the uncertainty does not matter for what we need to know. Other uncertainties can be reduced by further scientific work, such by more precise measurements with new instruments or by developing more sophisticated theories.

Total scepticism. There is a suspicion about the validity of most scientific knowledge, particularly that which is perceived to have philosophical, religious, or political implications.

Suspicion about science

In spite of the success of science at describing the material world and leading to powerful and useful technologies, there is much public suspicion of science. On the one hand, this is understandable given that science has led to technologies with undesirable health, environmental and social consequences. Some scientists, governments and companies have lied about these consequences and hidden them from the public. Human subjects have been abused in medical experiments. Drugs that were claimed to be effective and safe turned out to be ineffective or have undesirable side effects. Science has been used for ideological purposes. Sometimes scientists have faked results to advance their own careers. However, these failures should not undermine our trust in reliable scientific knowledge. Distinctions should be made between the bodies of knowledge, the applications of that knowledge, and the actions of institutions. I now discuss several common claims in public discussion that are used to justify scepticism of scientific knowledge.

Science is always changing. 

One day, scientists tell you that chocolate is good for your health, and the next year they say it is bad for you. And that is just the start. Then there are eggs, wine, running marathons, and cheese. They just can’t make up their mind. So why should we trust them? At one time, they believed in phlogiston and the aether. Now they say they don’t exist. Aristotle was replaced by Newton, who was replaced by Einstein. So why believe in human-induced climate change, biological evolution, vaccines, the Big Bang theory, or Einstein’s theories?

It is true that scientific knowledge does develop and change over time. However, today we have incredibly detailed observations and theories in physics, astronomy, chemistry, biology, and geology. Any future changes will be relatively minor because they will have to be consistent with all the knowledge we have now. Furthermore, when theories change, such as when Einstein superseded Newton, they don’t show that the old theory was completely wrong, but rather that it applied in a limited domain. For example, Newton’s theories of motion and gravity are extremely reliable when it comes to objects that are much larger than atoms, less dense than a black hole, and are moving at speeds less than about 10,000 kilometres per second. This is why engineers spend years learning Newton’s theories, not Einstein’s. If you want to build a good bridge or a rocket, Newton is good enough. He is not wrong.

Update. (Jan. 19). I just discovered that the NY Times had a recent op-ed Science Keeps Changing. So Why Should We Trust It?

“Well, that’s just a theory.” 

In popular debate, such a refrain may be applied to the theory of biological evolution, the Big Bang theory in cosmology, or human-induced climate change. The claimant usually wants to dismiss a particular theory as just idle speculation. Here, the term “theory” is used in the same sense as everyday speculations, such as “I have a theory as to why the president resigned,” or “I have a theory about why my computer is running so slowly.” These are just stories that sound somewhat plausible. In contrast, scientific theories in physics, such as quantum theory and Einstein’s theories of relativity, have precisely defined mathematical formulations that have been checked for logical consistency, made specific predictions, and tested to great precision in experiments. They are not “just theories.” For example, for the Big Bang theory about the beginning of the universe and Darwin’s theory of biological evolution and diversity, there are many independent lines of evidence that are consistent with each theory.  

Scientists cannot be trusted. 

They are not committed to the truth, but rather to their own interests and agendas, related to their careers, politics, and religion. They close ranks and support the status quo of current scientific “dogma”, rather than being open to original thinkers who critique it and propose alternative theories. They don’t want to lose their well-paid jobs and lucrative grants. 

On the one hand, scientists can be conservative and resistant to new ideas. On the other hand, there are significant career incentives to overturn existing knowledge and have your radical new theory accepted. That is how some scientists become famous and win Nobel Prizes. The reasons it does not happen very often are not necessarily for social or ideological reasons. Many of the theories we have today can explain an awful lot. It requires a lot of evidence, carefully acquired and checked, to convince people that those theories need to be modified, let alone abandoned. This may take decades. But it does happen. An example is the Big Bang theory of the universe, whose acceptance was initially resisted because it went against the prevailing view that the universe did not have a beginning. In biology, the discovery in 1970 of the enzyme reverse transcriptase went against a popular version of the “Central dogma” of molecular biology that DNA was always converted to RNA and not the reverse. That discovery led to a Nobel Prize.

I don’t trust scientists. I will do my own research. There is lots of good material from unbiased sources on the internet.

The internet provides a range of information and perspectives on practically any issue imaginable, including science. The material is particularly vast and controversial on biological evolution, the beginning of the universe, fundamental physics, the age of the earth, climate change, and medicine. Since the covid-19 pandemic, scepticism of the effectiveness and safety of vaccines has increased. 

Ivermectin is a drug that was developed as a treatment for parasite worms. Its incredible success was recognised by the award of the 2015 Nobel Prize in Physiology or Medicine to William Campbell and Satoshi Omura, who discovered the drug. During the pandemic, high-profile politicians and social media influencers promoted ivermectin as a treatment for covid-19, even after systematic medical studies showed it was ineffective. Recently, it has gained a reputation as a “miracle” drug that can even cure cancer, but this is being suppressed by the medical establishment. All clinical trials have shown the drug is ineffective for human ailments, beyond deworming. Nevertheless, there are groups on social media with hundreds of thousands of members that discuss the conspiracy, how to get the drug, and the experiences of participants using it to treat a wide range of ailments. Danny Lemoi, a founder of one of the largest groups, died in 2023 after taking massive daily doses of the drug for several years to treat a heart condition. Afterwards, one member of the group wrote “No one can convince me that he died because of ivermectin. He ultimately died because of our failed western medicine which only cares about profits and not the cure.”

Fans of ivermectin claim that they are escaping the biases and vested interests of the medical establishment and Big Pharma as they pursue the truth. However, they are not escaping bias and vested interests. Successful social influencers build their reputations and million-dollar incomes from promoting scepticism. If there is no conspiracy, just scientific uncertainty and occasional incompetence and malpractice, their following collapses. Populist politicians build their careers on criticism of and stoking resentment towards elites, such as the medical establishment. The authority of the medical establishment is replaced with the authority of the popular opinion of a group of people whose views are shaped by social media algorithms, intuition, and anecdotal experience.

My purpose in giving the example of Ivermectin is not to start a detailed critique of science scepticism. Rather, it is to illustrate the role that the interplay of trust, authority, and tradition plays in how we determine what is true and what to act on. There are two competing traditions here: the populism of alternative medicine and the elitism of professional medicine. Each has its own sources of authority. In the end, it boils down to who we trust. We do not have the time, energy, resources or inclination to check the veracity of every single piece of information we have access to. We take shortcuts. This is what tradition does for us, for better and worse. Thus, we cannot escape tradition. We are all swimming in traditions, many of which are in conflict with one another. The question is whether we are aware of it and what we do with that awareness.

2025 Nobel Prize in Physics: Macroscopic quantum effects

John Clarke, Michel H. Devoret, and John M. Martinis received the prize  “for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit.”

The work was published in three papers in PRL in 1984 and 1985. The New York Times has a nice discussion of the award, including comments from Clarke, Martinis, Tony Leggett, and Steve Girvin.

There is some rich, subtle, and beautiful physics here. As a theorist, I comment on the conceptual and theoretical side, but don't want to minimise that doing the experiments was a technical breakthrough.

The experiments were directly stimulated by Tony Leggett, who, beginning in the late 70s, championed the idea that Josephson junctions and SQIDs could be used to test whether quantum mechanics was valid at the macroscopic level. Many in the quantum foundations community were sceptical. Leggett and Amir Caldeira, performed some beautiful, concrete, realistic calculations of the effect of decoherence and dissipation on quantum tunneling in SQUIDs. The results suggested that macroscopic tunneling should be observable.

Aside: Leggett rightly received a Nobel in 2003 for his work on the theory of superfluid 3He. Nevertheless, I believe his work on quantum foundations is even more significant.

Subtle point 1. What do we mean by a macroscopic quantum state?

It is commonly said that superconductors and superfluids are in a macroscopic quantum state. Signatures are the quantisation of magnetic flux in a superconducting cylinder and how the current through a Josephson junction oscillates as a function of the magnetic flux through the junction. I discuss this in the chapter on Quantum Matter in my Very Short Introduction.

Leggett argued that these experiments are explained by the Josephson equations, which treat the phase of the superconducting order parameter as a classical variable. For example, in a SQUID, it satisfies a classical dynamical equation. 

If the state is truly quantum, then the phase variable should be quantised.

Aside: a nice microscopic derivation, starting from BCS theory and using path integrals, of the effective action to describe the quantum dynamics was given in 1982 by Vinay Ambegaokar, Ulrich Eckern, Gerd Schön

Subtle point 2. There are different signatures of quantum theory: energy level quantisation, tunnelling, coherence (interference), and entanglement.

In 1984-5, Clarke, DeVoret, and Martinis observed the first two. Macroscopic quantum coherence is harder to detect and was only observed in 2000. 

In a nice autobiographical article

Matchmaking Between Condensed Matter and Quantum Foundations, and Other Stories: My Six Decades in Physics

Leggett commented in 2020,

Because of the strong prejudice in the quantum foundations community that it would never be possible to demonstrate characteristically quantum-mechanical effects at the macroscopic level, this assertion made us [Leggett and Garg, 1985] the target of repeated critical comments over the next few years. Fortunately, our experimental colleagues were more open-minded, and several groups started working toward a meaningful experiment along the lines we had suggested, resulting in the first demonstrations (29, 30) of MQC [Macroscopic Quantum Coherence] in rf SQUIDs (by then rechristened flux qubits) at the turn of the century. However, it would not be until 2016 that an experiment along the lines we had suggested (actually using a rather simpler protocol than our original one) was carried out (31) and, to my mind, definitively refuted macrorealism at that level.  

I find it rather amusing that nowadays the younger generation of experimentalists in the superconducting qubit area blithely writes papers with words like “artificial atom” in their titles, apparently unconscious of how controversial that claim once was.

Two final comments on the sociology side.

Superconductivity and superfluidity have now been the basis for Nobel Prizes in six years and four years, respectively.

The most widely cited of the three PRLs that were the basis of the Prize is the one on quantum tunnelling with about 500 citations on Google Scholar. (In contrast, Devoret has more than 20 other papers that are more widely cited). From 1986 to 1992 it was cited about a dozen times per year. Between 1993 and 2001 is was only cited a total of 30 times. Since, 2001 is has been cited about 20 times per year.

This is just one more example of how citation rates are a poor measure of the significance of work and a predictor of future success.

Nobel Prize predictions for 2025

 This week Nobel Prizes will be announced. I have not done predictions since 2020. This is a fun exercise. It is also good to reflect on what has been achieved, including outside our own areas, and big advances from the past we may now take for granted.

Before writing this I looked at suggestions from readers of Doug Natelson's blog, nanoscale views, an article in Physics World, predictions from Clarivate based on citations, and recent recipients of the Wolf Prize.

Please enter you own predictions below.

Although we know little about how the process actually works or the explicit criteria used, I have a few speculative suggestions and observations.

1. The Wolf Prize is often a precursor.

2. Every now and then, they seem to surprise us.

3. Every few years, the physics committee seems to go for something technological, sometimes arguably outside physics, perhaps to remind people how important physics is to modern technology and other areas of science.

4. They seem to spread the awards around between different areas of physics.

5. Theory only gets awards when it has led to well-established experimental observations. Brilliant theoretical discoveries that motivate large research enterprises (more theory and experimental searches) are good enough. This is why predictions based on citation numbers may be misleading.

6. Once an award has been made on one topic, it is unlikely that there will be another award for a long time, if ever, on that same topic. In other words, there is a high bar for a second award.

7. I don't think the logic is to pick an important topic and then choose who should get the prize for the topic. This approach works against topics where many researchers independently made contributions that were all important. The awardee needs to be a standout who won't be a debatable choice.

What do you think of these principles?

For some of the above reasons, I discuss below why I am sceptical about some specific predictions.

My top prediction for physics is Metamaterials with negative refractive index, going to John Pendry (theory) and David Smith (experiment). This is a topic I know little about.

Is it just a matter of time before twisted bilayer graphene wins a prize? This might go to Allan MacDonald (theory) and Pablo Jarillo-Herrero (experiment). They recently received a Wolf Prize. One thing that convinced me of the importance of this discovery was a preprint on moiré WSe2 with beautiful phase diagrams such as this one.

The level of control is truly amazing. Helpful background is the recent Physics Today article by Bernevig and Efetov.

This is big enough to overcome 6. and the earlier prize for graphene.

Unfortunately, my past prediction/wish of Kondo and heavy fermions won't happen as Jun Kondo died in 2022. This suggestion also always went against Principle 6, with the award to Ken Wilson citing his solution of the Kondo problem.

The prediction of Berry and Aharonov for topological phases in quantum mechanics is reasonable, except for questions about historical precursors.

The prediction of topological insulators is going against 6. and the award to Haldane in 2016.

Clarivate's predictions of DiVincenzo and Loss (for qubits based on electron spin in quantum dots) goes against 5. and 7. It is just one of many competing proposals for a scaleable quantum computer and a large-scale device is still elusive.

Predictions of a prize for quantum algorithms (Shor, Deutsch, Brassard, Bennett) go against 5. 

Chemistry 

I don't know enough chemistry to make meaningful predictions. On the other hand, in 2019 I did correctly predicted John Goodenough for lithium batteries.  I do like the prediction from Clarivate for Biomolecular condensates (Brangwynne, Hyman, and Rosen). I discussed them briefly in my review article on emergence.

What do you think about my 7 "principles"?

What are your predictions?

Colloquium on 2024 Nobel Prizes

This friday I am giving a colloquium for the UQ Physics department.

2024 Nobel Prizes in Physics and Chemistry: from biological physics to artificial intelligence and back

The 2024 Nobel Prize in Physics was awarded to John Hopfield and Geoffrey Hinton “for foundational discoveries and inventions that enable machine learning with artificial neural networks.” Half of the 2024 Chemistry prize was awarded to Dennis Hassabis and John Jumper for “protein structure prediction” using artificial intelligence. I will describe the physics background needed to appreciate the significance of the awardees work. 

Hopfield proposed a simple theoretical model for how networks of neurons in a brain can store and recall memories. Hopfield drew on his background in and ideas from condensed matter physics, including the theory of spin glasses, the subject of the 2021 Physics Nobel Prize.

Hinton, a computer scientist, generalised Hopfield’s model, using ideas from statistical physics to propose a “Boltzmann machine” that used an artificial neural network to learn to identify patterns in data, by being trained on a finite set of examples. 

For fifty years scientists have struggled with the following challenge in biochemistry: given the unique sequence of amino acids that make up a particular protein can the native structure of the protein be predicted? Hassabis, a computer scientist, and Jumper, a theoretical chemist, used AI methods to solve this problem, highlighting the power of AI in scientific research. 

I will briefly consider some issues these awards raise, including the blurring of boundaries between scientific disciplines, tensions between public and corporate interests, research driven by curiosity versus technological advance, and the limits of AI in scientific research.

Here is my current draft of the slides.

John Hopfield on what physics is

A decade ago John Hopfield reflected on his scientific life in Annual Reviews in Condensed Matter Physics, Whatever Happened to Solid State Physics?

"What is physics? To me—growing up with a father and mother who were both physicists—physics was not subject matter. The atom, the troposphere, the nucleus, a piece of glass, the washing machine, my bicycle, the phonograph, a magnet—these were all incidentally the subject matter. The central idea was that the world is understandable, that you should be able to take anything apart, understand the relationships between its constituents, do experiments, and on that basis be able to develop a quantitative understanding of its behavior. 

Physics was a point of view that the world around us is, with effort, ingenuity, and adequate resources, understandable in a predictive and reasonably quantitative fashion. Being a physicist is a dedication to the quest for this kind of understanding."

He describes how this view was worked out in his work in solid state theory and moved into biological physics and the paper for which he was awarded the Nobel Prize. 

"Eventually, my knowledge of spin-glass lore (thanks to a lifetime of interaction with P.W. Anderson), Caltech chemistry computing facilities, and a little neurobiology led to the first paper in which I used the word neuron. It was to provide an entryway to working on neuroscience for many physicists..."

After he started working on biological physics in the late 1970s he got an offer from Chemistry and Biology at Caltech and Princeton Physics suggested he take it. 

"In 1997, I returned to Princeton—in the Molecular Biology Department, which was interested in expanding into neurobiology. Although no one in that department thought of me as anything but a physicist, there was a grudging realization that biology could use an infusion of physics attitudes and viewpoints. I had by then strayed too far from conventional physics to be courted for a position in any physics department. So I was quite astonished in 2003 to be asked by the American Physical Society to be a candidate for vice president. And, I was very happy to be elected and ultimately to serve as the APS president. I had consistently felt that the research I was doing was entirely in the spirit and paradigms of physics, even when disowned by university physics departments."

2024 Nobel Prize in Physics

 I was happy to see John Hopfield was awarded the Nobel Prize in Physics for his work on neural networks. The award is based on this paper from 1982

Neural networks and physical systems with emergent collective computational abilities

One thing I find beautiful about the paper is how Hopfield drew on ideas about spin glasses (many competing interactions lead to many ground states and a complex energy landscape).

A central insight is that an efficient way to store the information describing multiple objects (different collective spin states in an Ising model) is in terms of the inter-spin interaction constants (J_ij's) in the Ising model. These are the "weights" that are trained/learned in computer neural nets.

It should be noted that Hopfield's motivation was not at all to contribute to computer science. It was to understand a problem in biological physics: what is the physical basis for associative memory? 

I have mixed feelings about Geoffrey Hinton sharing the prize.  On the one hand, in his initial work, Hinton used physics ideas (Boltzmann weights) to extend Hopfields ideas so they were useful in computer science. Basically, Hopfield considered a spin glass model at zero temperature and Hinton considered it at non-zero temperature. [Note, the temperature is not physical it is just a parameter in a Boltzmann probability distribution for different states of the neural network]. Hinton certainly deserves lots of prizes, but I am not sure a physics one is appropriate. His work on AI has certainly been helpful for physics research. But so have lots of other advances in computer software and hardware, and those pioneers did not receive a prize.

I feel a bit like I did with Jack Kilby getting a physics prize for his work on integrated circuits. I feel that sometimes the Nobel Committee just wants to remind the world how physics is so relevant to modern technology.

Ten years ago Hopfield wrote a nice scientific autobiography for Annual Reviews in Condensed Matter Physics,

Whatever Happened to Solid State Physics?

After the 2021 Physics Nobel to Parisi, I reflected on the legacy of spin glasses, including the work of Hopfield.

Aside: I once pondered whether a chemist will ever win the Physics prize, given that many condensed matter physicists have won the chemistry prize. Well now, we have had an electronic engineer and a computer scientist winning the Physics prize.

Another side: I think calling Hinton's network a Boltzmann machine is a scientific misnomer. I should add this to my list of people getting credit for things that did not do. Boltzmann never considered networks, spin glasses or computer algorithms. Boltzmann was a genius, but I don't think we should be attaching his name to everything that involves a Boltzmann distribution. To me, this is a bit like calling the Metropolis algorithm for Monte Carlo simulations the Boltzmann algorithm. 

Autobiography of John Goodenough (1922-2023)

 John Goodenough was an amazing scientist. He made important contributions to our understanding of strongly correlated electron materials, magnetism, solid state chemistry, and materials science and engineering. He developed materials that are widely used in computer RAMs and rechargeable lithium batteries. He kept working in the laboratory and writing papers into his early 90s. Goodenough was awarded the Nobel Prize in Chemistry in 2019. Here is his Nobel Lecture, including text, slides, and video.

In 2008 he published Witness to Grace, a brief autobiography that chronicles his personal, scientific, and spiritual journeys. It is a fascinating story. The book is now out of print and the publisher is out of business. I have scanned a copy. You can download it here. I thank David Purdy for bringing to my attention the need to preserve the book.

Emergence talk at University of the Philippines

Today I am giving a seminar on emergence at the University of Philippines Los Banos, in the Institute of Mathematical Sciences and Physics.

Here are my slides.

Amazing things about Chandrasekhar's white dwarf mass limit

This is ultra-condensed matter physics!

In 1931, Subrahmanyan Chandrasekhar published a seminal paper, for which he was awarded the Nobel Prize in 1983. He showed that a white dwarf star must have a mass less than 1.4 solar masses, otherwise it will collapse under gravity. White dwarfs are compact stars for which the nuclear fuel is spent and electron degeneracy pressure prevents gravitational collapse. 

The blog Galileo unbound has a nice post about the history and the essential physics behind the paper.

There are a several things I find quite amazing about Chandrasekhar's derivation  and the expression for the maximum possible mass. 

m_H is the mass of a proton. M_P is the Planck mass. The value of the mass limit is about 1.4 solar masses.

Relativity matters

If the electrons are treated non-relativistically then there is no mass limit. However, when the star becomes dense enough the Fermi velocity of the electrons approaches the speed of light. Then relativistic effects must be included.

A macroscopic quantum effect

Degeneracy pressure is a macroscopic quantum effect. The expression above involves Planck's constant.

Quantum gravity

The mass formula involves the Planck mass, M_P.  On the one hand, this phenomena does not involve quantum gravity because there is no quantisation of the gravitational field. On the other hand, the effect does involve the interplay of gravity and quantum physics.

A "natural" scale

Formula that involve Planck scales usually represent scales of length, energy, mass, time, and temperature that are "unreal", i.e., they are vastly different from terrestial and astrophysical phenomena. For example, the temperature of the Hawking radiation from a black hole of one solar mass is 60 nanoKelvin. 

In contrast, the limiting mass is on the same scale as that of our own sun!

It agrees with astronomical observations

Determinations of the masses of hundreds of white dwarfs show most have a mass of about 0.5 solar masses and the highest observed value is 1.3 solar masses.

Eight amazing things physics has taught us

What are the most amazing things that we know about the physics of the universe? If you were to pick ten what would they be?

I recently read Fundamentals: Ten Keys to Reality (2021) a popular science book by Frank Wilczek. My interest in the book was piqued just to see what Wilczek's choices for his "ten" were. I got a copy from the public library and became entranced because I discovered what a gifted writer and expositor Wilczek is. I found I was learning some physics I did not know; or at least getting a deeper understanding of what I should know. I then bought my own copy so I could annotate it. I have previously enjoyed the insights in many of Wilczeks' Physics Today columns.

The book gives a popular presentation of some physics "basics" such as celestial mechanics, the Standard Model of elementary particles (which he renames the Core), and Big Bang cosmology.  I found it full of insights. I also appreciated that Wilczek does not have the hard reductionist or scientism edge found in the popular books of some distinguished theoretical physicists such as Weinberg and Hawking. However, a careful reading led me at times to be somewhat disappointed and irritated, for reasons that I discuss briefly below. In the end, this is because, not surprisingly, I have a much more emergentist perspective on reality, seeing it as stratified.

First, here are the ten things that Wilczek finds amazing, helpfully summarised in his chapter titles.

Part I. What There Is 

Chapter 1. There's Plenty of Space

Chapter 2. There's Plenty of Time

Chapter 3. There Are Very Few Ingredients

Chapter 4. There Are Very Few Laws

Chapter 5. There's Plenty of Matter and Energy

Part II. Beginnings and Ends 

Chapter 6. Cosmic History is an Open Book

Chapter 7. Complexity Emerges

Chapter 8. There's Plenty More to See

Chapter 9. Mysteries Remain

Chapter 10. Complementarity Is Mind-Expanding

Here are some of the ideas associated with each of the ten keys.

There's Plenty of Space

The scales of the universe are incredible. Beyond us, there is the vast numbers of stars and galaxies, and distances of more than ten billion light years. Within us, each of our bodies contains more atoms than there are stars in the universe. Our brains have as many neurons as there are stars in our galaxy. An atom is largely empty space.

There's Plenty of Time

Cosmic time is abundant. The quantity of time reaching back to the big bang dwarfs a human lifetime... [which] contains far more moments of consciousness than universal history contains human life spans. We are gifted with an abundance of inner time.

There Are Very Few Ingredients

Everything in the universe is made of just a few particles: leptons, quarks, and neutrinos. And forces and the associated bosons, such as photons, gravitons, and gluons. These particles have just a few properties: mass, charge, colour, and spin.

 "The most basic ingredients of physical reality are a few principles and properties. Four simple yet profound general principles govern how the world works.

1. The basic laws describe change.

2. The basic laws are universal.

3. The basic laws are local.

4. The basic laws are precise.

Newton realised locality was a problem. Fields rather than particles are the fundamenta building blocks of matter.

Quasiparticles are discussed. In high school, Wilczek was inspired by a visit to Bell Labs where he learnt that quanta of lattice vibrations are phonons. He describes how he introduced anyons in the early 1980s and how they were then identified with quasiparticles in fractional quantum Hall states.

There Are Very Few Laws

From forces we are led to fields, and from (quantum) fields, we are led to particles.

From particles we are led to (quantum) fields, and from fields, we are led to forces.

Thus, we come to understand that substance and force are two aspects of a common underlying reality.

The four fundamental forces (gravity, electromagnetism, weak nuclear, and strong nuclear) are described by just a few simple mathematical equations.

The art and science of spectroscopy is described as "Atoms sing songs that bare their souls, in light."

Wilczek's Ph.D. work on quark confinement and asymptotic freedom in Quantum Chromodynamics (QCD) was the beginning of QCD being accepted and used.

Newton's gravity theory presented the puzzle of the equivalence of inertial and gravitational mass. Einstein's gravity solved the puzzle and "fulfills Newton's aspiration for a theory of gravity based n local action". 

    "we can portray the majestic logic of general relativity in ten broad             strokes... "

    "John Wheeler, the poet of relativity, summed it up this way: "Space-time     tells matter how to move; matter tells space-time how to bend."

Wilczek makes the debatable and misleading claim that "The equations of QED, QCD, general relativity, and the weak force, ... have powered many advances, including lasers, transistors, nuclear reactors, MRIs, and GPS."

There's Plenty of Matter and Energy

The fact that the amount of solar energy falling on the surface of the earth is vastly greater than current human energy consumption.

The concept of "dynamical complexity" is introduced but not defined. "Music and ritual are purified expressions of dynamical complexity."

"The principle that the essence of human purposes is experienced through flows of information in dynamic complexity, rather than through details of chemistry and physiology, is both mind-expanding and liberating. It challenges us to imagine how minds could emerge elsewhere in the universe, and it prepares us to embrace those minds within our circle of empathy."

To me, this is "mumbo jumbo" and reflects the muddled thinking that occurs when Wilczek wildly extrapolates from "fundamental" physics to broader and deeper questions about humanity. The last chapter has similar weaknesses.

Cosmic History is an Open Book

A lucid short summary is presented of big bang cosmology. What we know and why we know it. The chapter ends with a brief reference to Augustine's prescient insights about time. It is what clocks measure and so time did not exist before the beginning of the universe.

Complexity Emerges

How did the featureless simple "soup" that existed a million years after the big bang develop into the complex universe seen today with structures such as stars, galaxies, planets, and biological life? This short chapter (only eight pages) mostly talks about the role of gravity. The chapter could have been much richer by discussing the emergence of complexity in biology, psychology, and sociology. Again, simple laws can produce complex properties.

There's Plenty More to See

The discovery of the Higgs particle and gravitational wave astronomy are both described. Some speculations are made to connect "Quantum Perception and Self-Perception."

Mysteries Remain

What triggered the big bang? Could it hapen again?

Are there meaningful patterns hidden in the apparent sprawl of fundamental particles and forces?

How, concretely, does min emerge from matter? (Or does it?)

Wilczek describes violation of time reversal invariance (T) in elementary particle physics and the Peccei-Quinn proposal for a new field to explain this. The corresponding particle was dubbed the axion by Wilczek, which fulfilled his high school dream to give a particle that name when he encountered a laundry detergent with that name. The axion "cleans up a problem" in elementary particle physics.

Axions are candidates for dark matter.

Complementarity Is Mind-Expanding

Bohr's concept of complementarity (embodied in wave-particle duality in quantum theory) is embraced. 

Complementarity is the concept that one single thing, when considered from different perspectives, can seem to have very different or even contradictory properties. Complementarity is an attitude toward experiences and problems that Ive found eye-opening an extremely helpful. It has literally changed my mind. Through it, I've become larger: more open to imagination, and more tolerant.

I am no fan of this perspective. I am all for having an open mind, considering a range of perspectives, and living with dialectic (intellectual tensions). However, I do not use quantum theory to justify that. There is a multitude of moral, philosophical, social, and political reasons that provide much more compelling justifications for humility. Bohr's perspective and extrapolations from the atomic world to politics has a long and dubious history that has systematically been debunked by Mara Beller, including in Physics Today.  Nevertheless, these ideas just won't go away, as seen why a recent volume of papers on Quantizing International Relations.

In summary, I love Wilczek's discussions of physics, and I think eight of the ten chapters describe amazing things about the physical world that we have learnt and should contemplate with awe and wonder.  But, two of the chapters make speculations about how the type of theoretical physics that Wilczek has made seminal contributions to is profoundly relevant to technological, social, economic, and political reality. I would much rather draw on the insights and debates from the humanities and social sciences to understand those realities and our place in them.

Colloquium on 2021 Nobel Prize in Physics II

 Here are the slides from today's talk.

Colloquium on 2021 Nobel Prize in Physics

 Every year the UQ Physics Department has a colloquium where someone describes the science behind the latest Nobel Prize. This year I am going to talk about Parisi and the spin glass problem. My colleague Henry Nourse will talk about the climate modelling part.

In preparation, I have found the book, Spin Glasses and Complexity by Daniel L. Stein and Charles M. Newman, very helpful. It is at the level of a colloquium and has a nice chapter on applications to other areas of science (e.g. proteins, simulated annealing, optimisation, computer science, ...) It enabled me to finally "understand" the background and significance of Hopfield's famous paper from 1982, "Neural networks and physical systems with emergent collective computational abilities".

Thinking about replica symmetry breaking has brought back memories of when I was a graduate student at Princeton. When I started Anderson was thinking about spin glasses a lot and had people working on it. I heard lots of talks about spin glasses, replica symmetry breaking, travelling salesmen, ultrametricity, ... Even David Gross gave a colloquium about work he did on spin glasses, with a very warm introduction by Phil. ["I introduce David Gross the condensed matter theorist"] However, once the cuprates happened at the end of 1986, Anderson seemed to largely drop the spin-glass work. Except for Dan Stein, everyone started working on cuprates. In hindsight, I wonder if that was a mistake. In particular, it might have been better for many of his students if they had worked on complexity rather than cuprates.

Next week I will post a draft of my slides. In the meantime, two questions for readers:

1. What are some specific questions you might like answered in such a colloquium?

2. What are some specific resources you may have come across about this year's prize that you found helpful or interesting?

Here are the slides.

2021 Nobel Prize in Physics: from spin glasses to complexity theory

I was delighted to hear of the award of the Nobel Prize in Physics for 2021. The committee continues to surprise us. I did not make any predictions this year, because I had nothing new to predict. I am still surprised that experimental tests of Bell inequalities (Aspect, Clauser, Zeilinger) have still not got a prize. Maybe next year.

Here I will just write about the award to Giorgio Parisi “for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales” as it involves condensed matter theory, beginning with spin glasses, and like many things with Phil Anderson!

The popular science background and the scientific background to the prize are worth reading, as always. It notes that in a Physics Today column Anderson wrote in 1988,

“The history of spin glass may be the best example I know of the dictum that a real scientific mystery is worth pursuing to the ends of the Earth for its own sake, independently of any obvious practical importance or intellectual glamour.” 

This was in the first of a series of seven Reference Frame columns he wrote on spin glasses. The fifth column described the work of Parisi.

Here I will describe the basic ideas, particularly as they show that sometimes obscure basic science questions, very abstract ideas and mathematical formulations can be useful for very practical scientific questions, across a wide range of disciplines.

A spin glass is a distinct state of matter. This means, that in terms of the Landau paradigm, there must be an order parameter and an associated broken symmetry. What are they? Parisi found the answers.

First, as one usually does in theoretical condensed matter, one needs to write down a minimal model Hamiltonian that is complex enough to capture the essential physics but is simple enough to be amenable to analytical and/or computational analysis. 

Sam Edwards and Anderson proposed the following model for a spin glass, and Ising model where the spins are on a regular lattice but the interaction between any pair of spins, J_ik, is a random Gaussian variable with zero mean and non-zero variance.

This means that the interspin interactions are equally likely to be ferromagnetic or antiferromagnetic, leading to significant frustration.

To solve such a model one needs to calculate the partition function Z for each realisation of the J's (disorder), calculate F=- T ln Z, and average over all the configurations of disorder. 

Averaging Z over disorder is just a Gaussian integral, but averaging ln Z is analytically intractable.

Anderson's physical intuition was combined with the mathematical trickery of Edwards, that he had cultivated with his earlier work on quantum field theory and soft matter.

The replica trick is based on an identity that one learns in introductory calculus.

One considers not one system but rather n identical copies (replicas) of the physical system, calculates the average of the partition function for this fictional n-system, and then treats n as a continuous analytical variable and takes the limit that n goes to zero in the formula above. Wow, that is abstract! But, it is tractable.

Personal aside: more than twenty years ago I learned and used the replica trick because (like supersymmetry) as it provides a powerful mathematical tool to treat disorder exactly in one-dimensional models. But, the spin-glass case is much richer and more subtle.

Strange things happen for the spin glass. Soon after Edwards and Anderson's work, Thouless, Anderson, Palmer, and others made the rather puzzling discovery that not all the replicas were the same below the temperature associated with transition to the spin-glass state. The replica symmetry was broken in the spin-glass state.

Parisi proposed the order parameter below for this broken symmetry state. i denotes a lattice site, and the indices alpha and beta denote replicas. When alpha and beta have different values, the order parameter only becomes non-zero when the replicas are different.

Parisi, Toulouse, Mezard, and others then showed that there is a hierarchical structure associated with the order parameter leading to the concept of ultrametricity which can be associated with the rugged energy landscape of not just the spin-glass problem, but also optimisation problems, simulated annealing, protein folding, neural networks, ...

A nice overview that puts the theory of spin glasses in a much broader scientific context is Physics and Complexity by David Sherrington.

On Doug Natelson's blog, nanoscale views, there is a nice discussion in the comments about Parisi's Nobel and the subtle issue of the connections between separation of time scales and ultrametricity, and the connections (or not) between Parisi and climate science.

Is condensed matter physics too abstract?

Condensed matter physics is about the properties of real materials. Real stuff that you can see and touch and that you can use to make very practical things like TV screens and mobile phones. Yet, I find it fascinating and somewhat ironic that in condensed matter theory very abstract ideas and mathematical techniques keep cropping up (and being extremely useful): variable spatial dimensions, imaginary frequencies, topology, Chern numbers, conformal invariance, ...

Yet, there is a danger with abstraction. Theoretical condensed matter is not pure mathematics. Perhaps, too often fancy and beautiful mathematics is prized over physical intuition and insight. Theory may take precedence over experiment. How does one find the appropriate balance?

This is part of broader issues about the role of abstraction and formality in education.

Pierre de Gennes (1932-2007) was arguably the founder of soft matter as a research field, as recognized by the Nobel Prize in Physics in 1991. He began his career working on superconductivity and went on to develop a unified framework to understand soft matter (liquid crystals, polymers, foams, colloids...), introducing ideas such as order parameters, scaling, renormalisation, and universality.

After his Nobel, de Gennes gave many lectures in French high schools, which were then published as a book, Fragile Objects: Soft Matter, Hard Science, and the Thrill of Discovery. I highly recommend it, both as a popular introduction to soft matter, but also to hear the perspective of a great scientist on education and research.

de Gennes spent almost his whole life living and working in France. In the book he rants about the French system, particularly its obsession with entrance exams, mathematics, formality, and the abstract.

“Manual skills, visual acumen, the sense of observation, an interest for the physical world which surrounds us, are all qualities that are neglected or downgraded.”

“To work in a garage seems to me the best initiation to a professional life.”

“Ignorance of the real world causes grave distortions.”

“the positivist prejudice”

I found this fascinating because one thing de Gennes is famous for is showing how some properties of a polymer can be understood by considering a theory involving a vector of dimension n, where n was a continuous variable, in the limit where n approaches zero! That is pretty abstract! But, I guess the point is that he is not against abstraction, exams, and mathematics, per se. Rather, he is against them taking on a life of their own.

de Gennes concerns are also shared by Henri Alloul (well known for beautiful NMR experiments on strongly correlated electron materials) author of Introduction to the Physics of Electrons in Solids. In the Preface, he writes, 

In many countries, teaching traditions have always given pride of place to a formal, and essentially deductive, presentation of the physics, i.e., starting from formal hypotheses and leading up to observable consequences. This deductive approach leaves a purely a posteriori verificational role to observation, and hides the thinking that has gone into building up the models in the first place. Here we shall adopt the opposite approach, which begins with the fact that in science in general, and in solid state physics in particular, the qualitative understanding of a phenomenon is an important step which precedes the formulation of any theoretical development. We thus urge the reader to carry out a careful examination of the deeper significance of experimental observations, in order to understand the need for specific models and carry out realistic approximations.

The debate about abstract mathematics is also central to contrasting views about the Institute for Advanced Study at Princeton.

de Gennes's views would have also resonated with Harry Kroto who shared The Nobel Prize in Chemistry for the discovery of buckyballs. He credited playing with Meccano as a child as very important in his scientific development.

Fifty years ago: three big discoveries in condensed matter

For the marketing plan for my Very Short Introduction, I was recently asked whether there were any significant anniversaries happening in condensed matter physics (and associated conferences). This is not something I normally think about.

I realised that fifty years ago there were three big discoveries. All eventually led to Nobel Prizes. Each discovery had a profound effect on the formation of condensed matter as a distinct discipline built around a few unifying concepts. At the time the discoveries and ideas appeared quite independent, but there are deep connections between them.

Renormalisation group and critical phenomena

In 1971 Ken Wilson published two papers  [PRB 4, 3174, and PRB 4, 3184] laying the foundations, followed by two PRLs in 1972, including one with the provocative title, Critical Exponents in 3.99 Dimensions. 

Wilson received the Nobel Prize in 1982. This work had many implications and applications. 

Explained universality in critical phenomena.

Highlighted how spatial dimensionality changes physics.

Illustrates why effective Hamiltonians work (so well).

Showed the power of quantum field theory techniques.

Defined concepts of scaling and fixed points.

Superfluidity in liquid 3He

In 1972,  Osheroff, Richardson, and Lee reported new phase transitions in liquid/solid 3He. Tony Leggett identified these transitions as due a superfluid phases and also identified the order parameters. The experimentalists shared the Nobel Prize in 1996 and Leggett in 2003. The discovery was significant for many reasons, beyond just being a new state of matter.

It provided a rich example of a state of matter with multiple broken symmetries. The order parameter has eighteen components, which can be viewed as a combined superfluid, ferromagnet, and liquid crystal.

The rich order parameter led to an exploration of diverse topological defects, from superfluid vortices with magnetic cores to boojums. This highlighted the concepts of broken symmetry, rigidity, and topological defects.

This was the first example of an unconventional fermionic superfluid. Specifically, it could be described by BCS theory, but not with s-wave pairing nor with the pairing mechanism of the electron-phonon interaction in elemental superconductors. This showed the adaptability of BCS theory. It laid the groundwork for understanding unconventional superconductivity in heavy fermions, organics, and cuprates.

Berezinskii-Kosterlitz-Thouless phase transitions

In Berezinskii published papers in 1970 and 1971, and Kosterlitz and Thouless published papers in 1972 and 1973. This work was significant for reasons including the following.

It showed states of matter and phase transitions were qualitatively different in two and three dimensions.

New concepts such as topological order, quasi-long-range order, essential singularities, and defect-mediated phase transitions were introduced.

Like that of Wilson, this work highlighted universality. There were connections between superfluids, superconductors, and XY magnets.

Scaling equations provided insight.

Kosterlitz and Thouless were awarded the Nobel Prize in 2016

We should celebrate!

Wow! Quite the Golden Jubilee!

Does anyone know of any conferences, events, or books that are planned to mark these anniversaries?