## Thursday, April 15, 2021

### 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 PRB's laying the foundations, followed by two PRLs in 1972. He 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 as due 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 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 1971 Berezinskii published his paper, 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?

## Monday, April 12, 2021

### Time management and stress reduction

I am not the greatest manager of my time. I am easily distracted and too often ruled by the tyranny of the urgent. I let the good become the enemy of the excellent. I look at my email too often...

Here are just a few points that I do find helpful to keep in mind and act on. They not only lead to better use of time but also reduce stress. I struggle with all of them.

1. It can wait.

We live in an urgent world with many people and tasks demanding immediate attention. There are some very rigid deadlines, such as for most grant applications. However, there are many other tasks such as submitting a paper, checking an experiment, replying to an email, ... that can wait for another today. It is time to log off, literally and mentally and relax. The world will not fall apart if you wait another day, week, or even month.

2. Delegate

Do I personally need to do this task or take on this responsibility? Is there someone else who is able and available to do it instead? Might they actually do it better than me? Even if they might not do it as well, would it be better that they do it anyway and free me up to do more important things?

Having said this, I am slow learn and have become aware that there are some cautions needed in delegating.

First, suppose I delegate to a person of lower "authority" than me, but who I have full confidence in. Others may not think they have the appropriate authority and so may be reluctant to act on or support what my delegate is.

Second, delegating tasks is no good if the person does not have the time, energy, and resources to complete the tasks. I may also need to provide the necessary resources and help them to see how they might delegate some tasks too.

3. Before embarking on a task, large or small, be clear on what your goal is.

This reduces the chance of getting distracted. Here is a concrete example. I often want to look for a paper on a specific question I have. Yet, I find that an hour later I am looking at my fourth paper because I got distracted by something I found interesting... and I have forgotten my initial question.

Some earlier thoughts on time management are here.

I welcome other suggestions.

## Thursday, April 1, 2021

### Where might condensed matter physics be heading?

Will there be big new discoveries? Will old problems be solved?

I have finished my draft of, "An endless frontier" the last chapter of Condensed Matter Physics: A Very Short Introduction.

I aim to give a balanced perspective that is optimistic but realistic. Have I? Obviously, this is highly subjective.

I am interested in general feedback, particularly on whether your aunt or uncle or an eager undergraduate would find this interesting and engaging.

Besides your own research area :), are there particular topics that you think are ripe for exploration?

Perhaps, a cartoon about predicting the future. Maybe one of these two?

## Tuesday, March 30, 2021

### Life transitions

Sometimes I never get around to writing or finishing planned blog posts. Last month something changed, but nothing changed for me. None of this is covid-related.

Three years ago I negotiated with my university a "transition to retirement" contract. These seem to be designed by the accountants to incentivize "highly paid old farts" to retire (regardless of whether they have anything to contribute) and make the university "financially sustainable". I got to go half-time for three years with no teaching and administrative responsibilities.  (BTW. I actually love teaching. I just don't enjoy it or see the point when it becomes bureaucratic and/or students are disengaged.) Pretty strong incentive!

I did this for a multitude of reasons: mental health, other opportunities and priorities, an unwillingness to take on administrative roles that seem to be mostly implementing dubious management decisions, and general concerns about where Australian universities are heading...(money, management, marketing, and metrics)...  Taking long service leave helped clarify things. Since then the wisdom of decision for me personally has only been confirmed, particularly with covid and some family health issues. I could not imagine that I would have coped with having to teach online with two weeks notice. I admire those of you who have done it... And then there is all these other things in the background such as an opinion piece in The Wall Street Journal  and associated submissions to a recent parliamentary inquiry...

At end of February, the three years came to an end and I officially "retired" and became an Emeritus Professor. My wife says I have not "retired" but just changed to new responsibilities and income streams.  I agree.

I am 60. I consider myself very blessed and privileged that I am able to do this. Not everyone has this freedom. I had about 25 years in Australian universities and most of it was as "research faculty" and I was generously funded and so got to work with many excellent postdocs.

In the short term very little has changed (besides the paychecks). I still have an office, am finishing Condensed Matter Physics: A Very Short Introduction, and collaborating with Ben Powell's group on spin-crossover materials, and trying to write more blog posts. I think some of this work is the nicest I have been involved with. I also work half-time as a consultant for a Christian NGO on a project that combines some of my passions and concerns: science, theology, Jesus, and the Majority World. Again I feel privileged to have that opportunity.

I am hardly "a man of leisure," contrary to what one of my wife's friends said last week.

So what about this blog? I have no immediate plans to change anything. I would like to post more often but always seem too "busy" or spend too much time polishing posts...

## Thursday, March 25, 2021

### Isotope effects in spin crossover materials

A range of isotope substitution experiments have been performed on spin-crossover materials.
Just like for other systems such as superconductors their interpretation is subtle.

The first studies are reviewed in Section 2.3.5 of this review article.
Isotopic exchange was investigated for a tris(picolylamine)iron(II) system which exhibits a two-step spin transition. Results are shown in the figure below. Significant changes in the spin-state transition curve were observed only when the isotopic substitution (H/D and 14N/15N) was made for atoms directly involved in the hydrogen-bonding network that connects the spin-crossover molecules. For example, with C2H5OD/ND2 the crossover temperature was shifted to higher temperatures by about 15 K and the middle step was no longer present.

I would not have expected such a large effect given the chemical complexity of these systems and that the H atoms are not immediately bonded to the iron atoms which undergo the spin-state transition.

I now mention two other studies. They are particularly helpful because they also measured how the enthalpy and entropy change associated with the spin-state transtion changed with isotopic substitution.

Weber et al. studied the iron(II) spin-crossover complex [FeL1(HIm)2] and the deuterium-substituted [FeL1(DIm)2] where Him is (not a man but) imidazole. Both exhibit a single-step transition with hysteresis. H/D exchange decreased both the transition temperature and the hysteresis width by a few K. Deuteration decreased the value of the enthalpy and entropy differences between the low spin and high spin states (determined from differential scanning calorimetry) by about twenty and ten percent, respectively. (See Table 2 in the paper). They estimated an interaction parameter J = 560 K, indicating strong intermolecular interactions, which they attributed to a hydrogen bond. They reference some earlier studies showing how the magnitude of the ligand field in a transition metal complex can be modified by hydrogen bonds involving the complex.

Very recently, Jornet-Mollá et al. studied the iron(ii) salt [Fe(bpp)2](isonicNO)2·HisonicNO·5H2O, which with decreasing temperature undergoes a transition at 162 K. There is a width of about 5 K, associated with hysteresis. With deuteration, the transition temperature decreases to 155 K, the width increases to 7 K, and the enthalpy and entropy differences both increase by about fifteen percent. “Annealing the compound at lower temperatures results in a 100% LS phase that differs from the initial HS phase in the formation of a hydrogen bond (HB) between two water molecules (O4W and O5W) of crystallisation. Neutron crystallography experiments have also evidenced a proton displacement inside a short strong hydrogen bond (SSHB) between two isonicNO anions.”
I am particularly interested in this because of previous work I have done on strong hydrogen bonds.

Again I am surprised at the magnitude of these effects because the zero-point energy associated with the relevant H atoms is only a small fraction of the total zero-point energy and the entropy contribution from vibrations.

I now start a preliminary discussion of how these experiments might be interpreted in terms of an Ising model picture, such as in a recent preprint. The Hamiltonian is

where the pseudospin sigma=+1/-1 corresponds to high spin and low spin states.

The crossover temperature is independent of the Ising interactions J's and given by

Our results in Appendix A of the preprint imply that there should be no dynamical isotope effects on the J’s, i.e., provided other parameters such as structural details and bond lengths do not change with isotope substitution.

This does not rule out changes in the crossover temperature. Both the enthalpy and entropy differences can change with isotope substitution (as is observed). The former due to changes in zero-point energies, and the latter due to changes in the vibrational contribution to the entropy change.

## Friday, March 19, 2021

### Interpretation of isotope effects can be subtle

Isotopic substitution has provided significant insights into molecular and solid-state physics. This involves the substitution of particular atoms in a compound by the same chemical element with a different nuclear mass (i.e. a nuclear isotope). An example is hydrogen/deuterium substitution which has shown the significant role that quantum nuclear motion can play in hydrogen bonding, particularly in strong hydrogen bonds. Of particular relevance to the discussion below is that isotopic substitution does not only change vibrational frequencies but can also change bond lengths.

A key piece of evidence on the road to the BCS theory of superconductivity in 1957 was the observation of an isotope effect. In 1950 a shift in the transition temperature of mercury was observed, suggesting that superconductivity resulted from electron-phonon interactions, as argued by Frohlich that same year. In particular, the magnitude of the shift was consistent with theoretical work by Herbert Frohlich. (Whether he predicted or postdicted the observed effect is a matter of debate, as discussed by Jorge Hirsch.) BCS theory gives that $\Delta T_c/T_c = - {1/over 2} \Delta M /M$, which arises from the fact that phonon frequencies scale with $1/\sqrt{M}$, consistent with the mercury experiments.

However, in the 1960s there were many observations of “anomalous” isotope effects, particularly in transition metals, that were inconsistent with the prefactor in this equation. These anomalies were resolved by going beyond the BCS theory and allowing for strong-coupling effects. Following the discovery of cuprate superconductors in 1986, isotope effects were observed in some cuprates. However, the consensus now is that these observations do not support an electron-phonon mechanism for superconductivity but rather are due to structural changes due to the isotope substitution. For example, isotopic substitution changes the zero-point energy, and that can alter the unit cell volume and the hopping parameter t in a Hubbard model.

This illustrates that there are subtleties in interpreting isotope experiments. This is because there are both structural and dynamical isotope effects. Changes in isotope can lead to changes in structure, such as bond lengths or lattice constants, and even in changes in crystal symmetry. These structural changes arise because the equilibrium structure of the system is that which minimises the total energy of the system. The contribution to this energy from the zero-point energy of the atomic vibrations changes with isotope substitution and with bond lengths. Dynamical effects are those that involve exchange of phonons such as in superconductivity.

I am not sure how to sharpen this structural/dynamical or static/dynamical distinction. Or is it secondary and primary effects?

In the next post, I will discuss observations of isotope effects in spin-crossover materials and how that relates to recenttheoretical work with my collaborators.

## Wednesday, March 17, 2021

### Condensed matter physics in 250 words

How would you define condensed matter physics? In 250 words how might you motivate someone to want to know more. For Condensed Matter Physics: A Very Short Introduction,  I need to write a brief blurb (about 250 words) that will be used for marketing.

Here is my first attempt. What do you think?
There are many more states of matter than just solid, liquid, and gas. Examples include liquid crystal, magnet, glass, and superconductor. New states are continually being discovered leading to a stream of Nobel Prizes. Some states, such as superfluid and superconductor, exhibit the weirdness normally associated with the quantum physics of single atoms, such as Schrodinger's cat. Condensed matter physics seeks to understand how states of matter and their distinct physical properties emerge from the atoms that a material is composed of. Materials and states studied by condensed matter physicists are central to modern technology. Examples include superconductors in hospital MRI machines, magnetic multilayers in computer memories, LEDs in solid-state lights, crystalline silicon in computer chips, and liquid crystals in digital displays.

Condensed matter physics is not just defined by the objects that it studies (states of matter in materials), but rather by a particular approach to the study of these objects. It addresses fundamental questions and produces unifying concepts to describe a wide range of phenomena in materials that are chemically and structurally diverse.

A system composed of many interacting parts can have properties that the parts do not have. Water is wet, but a single water molecule is not. Your brain is conscious, but a single neuron is not. Such emergent phenomena are central to condensed matter physics and also occur in many fields, from biology to computer science to sociology, leading to rich intellectual connections. When do quantitative differences become qualitative differences? Can simple mathematical models describe rich and complex behaviour? What is the relationship between the particular and the universal? Condensed matter physics is all about these big questions.

If you gave the book to your aunt would this motivate her to start reading?

If your colleague in engineering was browsing in a book store and read this on the cover would they buy the book?

I welcome suggestions.

BTW. In case you were wondering, the book is not about to come out. I just need to submit the marketing plan to OUP.

## Monday, March 15, 2021

### Radioactive science for the masses

My wife and I watched the movie, Radioactive, based on the life of Marie Sklodowska Curie. She was an amazing scientist who showed incredible perseverance, particularly in the face of discrimination by the scientific establishment in France at the beginning of the twentieth century, and attacks in the media because of her gender, nationality, and personal life.

The movie is good entertainment and creative, maybe a bit too creative at times. But they be a matter of personal taste. There were many things that I learnt, some substantial and others just interesting trivia, particularly after reading more on Wikipedia. Here are a few.

Curie did not only discover radioactivity, the elements radium and polonium (named after her native Poland), but also was the founder of nuclear medicine.

One can easily forget that more than a century ago, chemistry labs were very basic and that producing pure samples was a tedious process. For example, a tonne of pitchblende (uranium oxide ore) had to be crushed and processed to produce just one-tenth of a gram of radium chloride.

Back then the boundaries between physics and chemistry were fuzzy. Marie received a Nobel Prize in both. I wonder whether the legacy of joint chemistry-physics institutes in France was essential to de Gennes's work in soft matter.

Both Curie's started out in solid-state physics. Pierre Curie and his older brother discovered piezoelectricity. Pierre discovered the transition temperature for ferromagnetism (Curie temperature), and the Curie law for the temperature dependence of the magnetic susceptibility in a paramagnet. He followed his wife into nuclear research.

After her husband's tragic death, she had an affair with Paul Langevin and was vilified in the press.

A strong critique of the movie is by Geraldine McGinty. On the one hand, I agree with her concerns. On the other hand, I am just happy that "Hollywood" is exposing people to this extraordinary woman and her science. Maybe my hopes and expectations are just too low.

This relates to an ongoing debate about to what extent movies based on historical figures have to be historically accurate in every detail. The Crown (which I love) has brought these debates to the fore. Simon Jenkins states The Crown's fake history is as corrosive as fake news. Recent movies about scientists also raise the question to what extent the science must be absolutely accurate.

What do you think?

I welcome other comments on the movie, particularly from women.

## Thursday, March 11, 2021

### PhD students and postdocs need to learn soft skills

Most Ph.D. students and postdocs will end up employed outside academia and doing work that is not related to their current research. For this reason alone it is important to learn a broad range of skills beyond what is needed to publish that paper in a luxury journal that their supervisor craves.

Furthermore, for faculty to survive, let alone flourish, in today's university (corporate) environment soft skills are very important.

David Sholl (a frequent commenter on this blog) has just published a relevant book. Here is the publisher blurb.

Long-term success in scientific research requires skills that go well beyond technical prowess. Success and Creativity in Scientific Research: Amaze Your Friends and Surprise Yourself is based on a popular series of lectures the author has given to PhD students, postdoctoral researchers, and faculty at the Georgia Institute of Technology. Both entertaining and thought-provoking, this essential work supports advanced students and early career professionals across a variety of technical disciplines to thrive as successful and innovative researchers.

If you read it please post some thoughts in the comments below.

## Friday, March 5, 2021

### Management is not leadership

Being in a management position is neither a necessary nor a sufficient condition for academic leadership.

Senior managers at Australian universities sometimes wax lyrical about how they are in leadership. When it comes to promotion decisions, they also judge junior academics on whether they show "leadership".  This seems to be equated with the size of one's research group and the number of one's citations. The rise of this fixation on "leadership" in universities was highlighted by a commenter on a recent post.

This misunderstanding is another example of how university management does not actually consider what their own academics in the university may actually know. Leadership is a well-researched topic. If managers talked to faculty in business and history, they might be told something along the following lines.

The cartoon is from here.

Real leadership is characterised by influence. It leads to change. Real leaders can motivate people to change their views and their lives. This is of substance, unlike "change management" which seems to me to be a euphemism for sacking people, changing lines of reporting, and renaming (rebranding) the names of departments and courses.

Real leadership is not about occupying a powerful position that you use to exert control over people. The authority that real leaders have is intellectual or moral authority, not legal authority.

Previously I posted about how humility and listening to others has been found to be a key ingredient of leadership, rather than self-promotion and defensiveness.

Consider Einstein working in the patent office, Douglas Hofstadter unemployed and living with his parents while writing Godel, Escher, Bach, the obscure virus club, Nelson Mandela in prison on Robben Island, and Gandhi on a hunger strike. None held formal positions of authority or commanded large salaries, budgets, or staff. But they were leaders. They influenced people.

Being in a management position or holding a political office does not mean you are a leader. Gorbachev and Brezhnev both held the same position (for 6 and 18 years respectively). Who was the real leader?

My postdoctoral mentor, the late John Wilkins, never held a management position, but he sure was a leader. He was influential for the good of others and for condensed matter physics.

I like the following text

Within minutes they were bickering over who of them would end up the greatest. But Jesus intervened: “Kings like to throw their weight around and people in authority like to give themselves fancy titles. It’s not going to be that way with you. Let the senior among you become like the junior; let the leader act the part of the servant."

## Tuesday, March 2, 2021

### Nobel prizes and condensed matter physics

In Condensed Matter Physics: A Very Short Introduction I would like to include an Appendix with a list of all the Nobel Prizes related to condensed matter physics. My list includes 31 in Physics and 6 in Chemistry. I acknowledge that a few in my list are debatable. Some of the Chemistry prizes were to people who trained in condensed matter physics but eventually worked in chemistry departments. A few of the physics prizes are closer to electronic engineering than condensed matter. On the one hand, Nambu was not a condensed matter physicist, but he took Anderson's ideas about broken symmetry in superconductivity and applied them to particle physics.

I want to include the list because I find it pretty amazing and it illustrates just how CMP consistently seems to turn up surprising new discoveries. Many of these prizes are mentioned in the text of the VSI.

In writing the book, and particularly the chapter on topological quantum matter, I found that nobelprize.org is very helpful. The popular descriptions for specific prizes contain helpful language, metaphors, images, and anecdotes. The technical descriptions give very nice introductions/summaries of the discoveries associated with the prize. Beginning Ph.D. students may find them very helpful.

## Thursday, February 25, 2021

### Introducing topological quantum matter

I just completed my first draft of Chapter 8: Topology Matters for Condensed Matter Physics: A Very Short Introduction.

Any comments and suggestions would be appreciated. I learned a lot writing the chapter, but imagine it needs to be made more accessible.

## Tuesday, February 23, 2021

### Is this sustainable?

This is a basic question that is worth asking in many situations and contexts. Here are some examples.

John is a postdoc who works seventy hours a week. He is always in the lab. He never takes holidays. He says he will once he gets a paper in a luxury journal. But, then we won't take a break until he gets a faculty job...

The students of Professor X regularly experience verbal abuse from him. He usually apologises for getting "carried away".

A government is corrupt, incompetent and tortures its political opponents and critics.

Suresh is on his fourth postdoc. Each has been in a different country.

Susan is a young faculty member, married and with two young children. She is usually at work or "on the road". At home she is mostly working.

A university borrows huge amounts of money from a bank in order to build very fancy buildings that they hope/claim will attract international students.

Scientists keep telling funding agencies that their research field is going to produce commercial benefits in just a few years.

Humans burn lots of fossil fuels....

Every year a university increases the administrative load on faculty by "just a few hours per week".

What will eventually happen? Something will break. A colleague once said to me "if you treat people like a machine and your drive them hard enough they will break. Just like a machine."

Eventually, we butt up against reality. It does not matter what we wish is true. The reality is that humans are finite. We have only finite physical, emotional, and mental resources. We all only have finite time, money, and abilities. Individuals, families, communities, institutions, and nations have only finite financial, social, and political capital.

Every situation is different. Every person is different. Our resources, whether financial or emotional, may differ significantly from one another. But we are all finite.

So, a good question to ask in any endeavor is "Is this sustainable?"

What do you think? Are there situations where you think this question should be asked?

## Wednesday, February 17, 2021

### Characteristics of emergent phenomena

A property of a system composed of interacting parts is emergent if it has the following characteristics. The property is

1. not present in the parts.

2. difficult to predict solely from knowledge of properties of the parts and how they interact with one another.

3. associated with a modification of the properties of and the relationships between the parts.

4. universal, i.e., it is independent of many of the details of the parts.

Different people have different views on what emergence is, particularly with regard to the second characteristic. “Difficult to predict” is sometimes replaced with “impossible”, “almost impossible”, or “extremely difficult”, or “possible in principle, but impossible in practice.” After an emergent property has been observed sometimes it can be understood in terms of the properties of the parts. An example is the BCS theory of superconductivity. This is a posteriori, rather than a priori, understanding. A key word in my statement is “solely”.

Examples of properties of a system that are not emergent are volume, mass, charge, and number of atoms. These are additive properties.

Associated with emergent properties are also unique entities, concepts, theories, and organizing principles.

What do you think?

The text above is taken from my first draft of Chapter 9: Emergence: More is Different for Condensed Physics: A Very Short Introduction. I posted it earlier, asking for feedback, but did not receive any. Since it is such a central chapter please do send some feedback, even if brief.

## Thursday, February 11, 2021

### Desperately seeking tantalum

The road from materials research to commercial technology is a complex and tortuous one. It is not just a matter of what is physically possible. There are rigorous criteria that must be met along the way: financially competitive, mass production, reliability, durability, non-toxicity, ...

The materials needed don't just have to be available, cheap enough, and sufficiently abundant. One also needs supply chains that are not only reliable but also ethical.

In The Economist there is a fascinating (and disturbing) article that shows the complexities involved with the supply chains for just one of the metals used in our smart phones.

Why it’s hard for Congo’s coltan miners to abide by the law
American rules against conflict minerals have unintended consequences.
Tantalum, a metal used in smartphone and laptop batteries, is extracted from coltan ore. In 2019 40% of the world’s coltan was produced in the Democratic Republic of Congo, according to official data. More was sneaked into Rwanda and exported from there. Locals dig for the ore by hand in Congo’s eastern provinces, where more than 100 armed groups hide in the bush. Some mines are run by warlords who work with rogue members of the Congolese army to smuggle the coltan out.

On the science side, I wrongly guessed that coltan was some compound containing cobalt and tantalum. It is actually a mixture of two distinct crystals, tantalite [(FeMn)Ta2O6] and columbite [(FeMn)Nb2O6].

On the economic side, I found it interesting that until a few years ago Australia actually supplied most of the world's coltan.

In terms of political economy, this problem is an example of the "resource curse", a common experience of countries in The Bottom Billion.

If you are concerned about these issues and you live in Europe you might consider buying a Fairphone.

## Monday, February 8, 2021

### The emergence of randomness

What is the relationship between deterministic and stochastic "laws" of motion?

Subtle. It is possible that random behaviour can emerge from underlying deterministic laws and the converse. Deterministic laws can emerge from a system of many interacting parts that are described by stochastic motion.

This is nicely discussed in a Physics Today, column by Leo Kadanoff from 2002. Here are a few quotes. First, he discusses how random behaviour, such as Brownian motion, can emerge from many particles undergoing deterministic motion, or stochastic motion...

the observation of apparently stochastic features in some behavior does not imply that the underlying laws are themselves probabilistic. Often, deterministic motion is so complex or so sensitively dependent on initial conditions that the motion is indistinguishable from a set of random events. For example, the path taken by an individual molecule in a gas is very well modeled as a random walk, entirely probabilistic in its nature.

The random walk model can be derived from more fundamental models of molecular scattering. The scattering events could be realized in at least three different ways: using classical mechanics (fully deterministic), using quantum mechanics (partially deterministic), or prespecifying the probabilities of scattering. Thus the probabilistic single-particle model, the random walk, can be equally well obtained from a many-particle model that is entirely deterministic, partially so, or not deterministic at all. Real gases will all show the same behavior independent of the detailed laws governing the scattering.

We use the word “universality” to describe the rather commonly occurring physical situations in which a set of derived laws remains substantially the same over a wide range of alternative underlying fundamental laws. In these cases, the observable outcome cannot be used to select among the possible underlying laws.

This universality is a characteristic of emergent phenomena. Laughlin and Pines refer to this as "protectorates": whereby the underlying physics is obscured by the phenomena that is observed at a higher level. For example, observation of acoustic modes in a crystal obscures the underlying atomic structure.

Kadanoff then discusses how deterministic laws can emerge from underlying stochastic ones.

Conversely,... if you put together many individual stochastic motions, you may well get an essentially deterministic situation. A dilute classical gas obeys the deterministic gas law, PV = NkT. Through the “miracle” of large numbers, many stochastic molecules have produced a deterministic gas.

Kadanoff's article is actually not primarily concerned with the issues of emergence. It is entitled, Models, Morals, and Metaphors, and is mostly concerned with possible philosophical implications of chance and probability playing a role in evolutionary theory.

## Friday, February 5, 2021

### Super-unconventional superconductivity

I was brought up to believe that spin-singlet superconductors must be s-wave (elemental) or d-wave (cuprates) and spin-triplet must be p-wave (superfluid 3He) or f-wave, and so on...  More generally, singlets (triplets) are associated with even (odd) parity.

However, like a lot of things we learn some of us tend to forget what are the necessary assumptions needed for the result/claim to be valid.

Thus, I was intrigued when my colleague Ben Powell showed me this preprint.

Unconventional superconductivity near a flat band in organic and organometallic materials
Jaime Merino, Manuel Fernandez Lopez, Ben J. Powell

For a t-t'-J model on a decorated honeycomb lattice, they find an f-wave spin-singlet superconductor!

The explanation for this surprise is as follows.

The Cooper wavefunction must always be anti-symmetric under fermion exchange. However,  additional internal degrees of freedom can change things.

Two other examples come to mind.

One is non-centrosymmetric superconductors, where the absence of inversion symmetry in the crystal, means that parity is no longer a good quantum number. Then spin-orbit coupling can lead to a pairing state which is a mixture of spin-singlets and spin-triplets.

The paper below argues that in multiorbital systems that new types of singlet pairing are possible, such as intra- and inter-orbital pairing. This may be relevant to some iron-based superconductors and heavy fermion superconductors. In particular, it can explain certain perceived inconsistencies between experimental results for different physical quantities. Some suggested an energy gap for quasi-particle excitations while others did not.

Multiorbital singlet pairing and d + d superconductivity
Emilian M. Nica & Qimiao Si

## Thursday, January 28, 2021

### Will there be big new discoveries in condensed matter physics?

There are two aspects to this question concerning the future of condensed matter physics. First, are there big things to be discovered? If yes, will they be discovered?

I believe the first answer is yes for two reasons. First, the past hundred years have given us a continual stream of discoveries, many of them unexpected. Every time that things get a little boring, pretty soon there is something exciting and new. Second, condensed matter physics is all about emergent phenomena in materials. Emergent phenomena are extremely hard to anticipate or predict. Because of the combinatorics of chemistry, the list of possible materials to study is endless. CMP presents an endless frontier to explore. However, just because such a frontier exists does not mean that it will be explored. Successful explorers require courage, creativity, resources, time, and freedom.

I am concerned that the wild frontiers of condensed matter may not be explored. It is worth reflecting on who were some of the pioneers of CMP and the character of their institutional environments.  Consider Kammerlingh Onnes, Landau, Kapitsa, Anderson, de Gennes, and Leggett. Some common elements of the context (institutional, historical, political) in which they made their discoveries were time, stability, job security, mental space, and intellectual freedom. For example, Anderson spent almost three decades at Bell Labs in its heyday. Thanks to the monopoly of Bell in providing telephone services in the USA, the parent company had a very secure and stable income, providing it the ability to provide substantial financial and institutional support for basic research.

These pioneers played a long game. They had the freedom to fail, to choose research topics, and to change directions. They did not follow fashion and were fiercely independent thinkers. Andrew Zangwill highlights this about Anderson in his biography. They largely had the resources they needed and did not have to worry or fight for funding. Their daily life was very different from that of a researcher today. Their mental space was not filled with an endless stream of distractions such as emails, grant proposals, conferences, reporting, reviewing, committees, metrics, ... Most of their time and mental energy was simply focused on curiosity-driven research.

Today, there is intense competition for funding, institutional status, and career benefits associated with obtaining it, and a pressure to produce in the short term "outputs" (papers) and "impact" (citations) and "national benefit" (technological, commercial, security, and social). This naturally leads to researchers working on "safe" projects in fashionable areas that they are confident will produce results in the short term.

I hope that I am wrong. But, I fear that great discoveries may be missed.

## Monday, January 25, 2021

### A popular introduction to emergence

Emergence is central to condensed matter physics. Furthermore, arguably emergence is one of the most important concepts to come from science in the second half of the twentieth century. Emergence is central to many of the big questions in the sciences, both natural and social.

Hence, it is natural that in Condensed Matter Physics: A Very Short Introduction, I am dedicating a whole chapter to the subject. Here is my draft.

I welcome comments and suggestions, particularly if you are not a condensed matter physicist.

## Wednesday, January 20, 2021

### Where is materials research heading?

One way to answer this question is to look at the reports prepared every decade by the National Academies in the USA. I have recently been looking through the 2019 report, Frontiers of Materials Research: A Decadal Survey.

There are several reasons why I like to look at these reports. A previous post mentioned a similar 2007 report prepared for the USA Department of Energy.

I can learn a lot about materials science and engineering. See, for example, the figure below.

The reports help put condensed matter physics in the broader context of research in materials science and engineering.

[Previously, I have argued that CMP is a particular approach to materials research and is distinct from materials physics. Although there is a significant overlap in the materials studied and some of the methods used, the driving questions are distinctly different].

The reports provide choice quotes for grant applications. Here is one from pages 24-25.

Key Finding: Basic research in fundamental science directions, meaning work that neither anticipates nor seeks a specific outcome, is the deep well that both satisfies our need to understand our universe and feeds the technological advances that drive the modern world. It lays the groundwork for future advances in materials science as in other fields of science and technology. Discoveries without immediate obvious application often represent great technical challenges for further development (e.g., high-Tc superconductivity, carbon nanotubes) but can also lead to very important advances, often years in the future.

Key Recommendation: It is critically important that fundamental research remains a central component of the funding portfolio of government agencies that support materials research. Paradigm-changing advances often come from unexpected lines of work.

Here is one from page 6.

Key Finding: Quantum materials science and engineering, which can include superconductors, semiconductors, magnets, and two-dimensional and topological materials, represents a vibrant area of fundamental research. New understanding and advances in materials science hold the promise of enabling transformational future applications, in computing, data storage, communications, sensing, and other emerging areas of technology. This includes new computing directions outside Moore’s law, such as quantum computing and neuromorphic computing, critical for low-energy alternatives to traditional processors. Two of NSF’s “10 big ideas” specifically identify support of quantum materials (see The Quantum Leap: Leading the Next Quantum Revolution and Midscale Research Infrastructure).

The reports are based on the consensus of a range of experts. Hence, they arguably more objective than survey articles written in luxury journals by individuals hyping their field.

But, right now the reason I am reading this report is that I am writing the last chapter of Condensed Matter Physics: A Very Short Introduction, and need to address the question of where CMP is heading. Some earlier preliminary thoughts are here.

Here are a few of my thoughts about this report. I would love to hear the perspectives of others.

First, I should give some important caveats. I have only skimmed the report. It was written by people who know much more than I. Writing a report that is based on a diverse community of interests and perspectives is extremely difficult. The main audience for such reports is not scientists themselves but rather funding agencies and policymakers.

A lot of attention is given to the potential of computational materials science, including when combined with data science methods (e.g. machine learning), topological matter, and quantum information processing in solid-state devices. However, I remain skeptical about the hype associated with these subjects, particularly with regard to technological applications. Big data need big theory too.

Significant attention is given to the relevance of materials research to USA defense, national security, and economic competitiveness. I wonder if this is because the report is being pitched to a MAGA government. Although I agree on the relevance, for many of us that is not the motivation for our interest in materials.

Update. In a comment below, David Sholl pointed out that NSF is not happy with the report. The background given there is also worth reading.

## Tuesday, January 12, 2021

### Emergence in biology

Emergence is one of the most important concepts developed by scientists in the second half of the twentieth century. Largely, independently of one another emergence was discussed, debated, and developed by physicists, biologists, social scientists, and philosophers.

Biology concerns phenomena at many different scales, some of which are nicely captured in the figure below, taken from here. At each scale, distinct phenomena emerge, with associated concepts, theories, and methods.

Ernst Mayr was one of the leading evolutionary biologists in the twentieth century and was influential in the development of the modern philosophy of biology. He emphasised the importance of emergence, contrasting the value of analysis with the limitations of reductionism (both defined below).

In Mayr's book, What Makes Biology Unique? Considerations on the Autonomy of a Scientific Discipline, chapter 4 is Analysis or Reductionism.

Needless to say, the workers in the more complex branches of science saw in this [reductionist] claim only a ploy of the chemists and physicists to boost the importance of their fields. As Hilary Putnam said correctly: “What [reductionism] breeds is physics worship coupled with neglect of the ‘higher-level’ sciences. Infatuation with what is supposedly possible in principle goes with indifference to practice and to the actual structure of practice” (1973).

What is the crucial difference between the concepts analysis and reduction? The practitioner of analysis claims that the understanding of a complex system is facilitated by dissecting it into smaller parts. Students of the functions of the human body choose as their first approach its dissection into bones, muscles, nerves, and organs. They make neither of two claims made by the reductionists
(A) that the dissection should proceed “down to the smallest parts,” – i.e., atoms and elementary particles, and
(B) that such a dissection will provide a complete explanation of the complex system.
This reveals the nature of the fundamental difference between analysis and reduction. Analysis is continued downward only as long as it yields useful new information and it does not claim that the “smallest parts” give all the answers.

... the view that composite wholes have properties not evident in their components has been widely accepted since the middle of the nineteenth century. The principle was already enunciated by Mill, but it was Lewes (1875) who not only presented a thorough analysis of the topic but also proposed the term emergence for this phenomenon.
... emergence is characterized by three properties
... first, that a genuine novelty is produced – that is, some feature or process that was previously nonexistent;
second, that the characteristics of this novelty are qualitatively, not just quantitatively, unlike anything that existed before;
third, that it was unpredictable before its emergence, not only in practice, but in principle, even on the basis of an ideal, complete knowledge of the state of the cosmos.

Mayr then discusses how in the first half of the twentieth century, emergence fell out of favour with biologists, such as J.B.S. Haldane, partly because the three characteristics above "appear at first sight to be in conflict with a straightforward mechanistic explanation."

How does this history relate to Phil Anderson and condensed matter physics?  This is nicely discussed by Andrew Zangwill in Chapter 12 of Mind over Matter. More is Different (1972) did not include the word emergence and Anderson did not use the term in print until 1981. Following Anderson's Nobel Prize in 1977, he received many invitations to speak to groups outside the physics community, including biologists, some of whom were fans of "More is Different".  This then exposed Anderson to the thinking and terminology of the biologists.

Aside: In a previous post, I discussed how Mayr described how prominent physicists such as Bohr and Schrodinger embraced vitalism.