Very Short Introductions Podcast on Condensed Matter Physics

The podcast episode where I talk about my book just came out.

It is available on a range of platforms, listed here, including SoundCloud and YouTube.

Emergence in nuclear physics

Nuclear physics exhibits many characteristics associated with emergent phenomena. These include a hierarchy of scales, effective interactions and theories, and universality.

The table below summarises how nuclear physics is concerned with phenomena that occur at a range of length and number scales. At each level of the hierarchy, there are effective interactions that are described by effective theories. Some of the biggest questions in the field concern how the effective theories that operate at each level are related to the levels above and below.

Moving from the bottom level to the second top level, relevant length scales increase from less than a femtometre to several femtometres.

The challenge in the 1950s was to reconcile the liquid drop model and the nuclear shell model. This led to the discovery of collective rotations and shape deformations. The observed small moments of inertia were explained by BCS theory. Integration of the liquid drop and shell models led to the award of the1975 Nobel Prize in Physics to Aage Bohr, Ben Mottelson, and Rainwater.

Since the 1980s a major challenge is to show how the strong nuclear force between two nucleons can be derived from Quantum Chromodynamics (QCD). The figure below illustrates how the attractive interaction between a neutron and a proton can be understood in terms of the creation and destruction of a down quark-antiquark pair. The figure is taken from here.

An outstanding problem concerns the equation of state for nuclear matter, such as found in neutron stars. A challenge is to learn more about this from the neutron star mergers that are detected in gravitational wave astronomy.

Characteristics of universality are also seen in nuclear physics. Landau’s Fermi liquid theory provides a basis for the nuclear shell model which starts from assuming that nucleons can be described in terms of weakly interacting quasiparticles moving in an average potential from the other nucleons. The BCS theory of superconductivity can be adapted to describe the pairing of nucleons, leading to energy differences between nuclei with odd and even numbers of nucleons. 

Universality is also evident in the statistical distribution of energy level spacings in heavy nuclei. They can be described by random matrix theory which makes no assumptions about the details of interactions between nucleons, only that the Hamiltonian matrix has unitary symmetry. Random matrix theory can also describe aspects of quantum chaos and zeros of the Riemann zeta function relevant to number theory.

Shape memory alloys

Recently I bought a small wire of NiTinol to have fun with and use in demonstrations to kids. This video gives a spectacular demonstration and attempts to explain how it works. I did not know about their use in stents for heart surgery.

I am still struggling to understand exactly how shape-memory alloys work. According to Wikipedia

The shape memory effect occurs because a temperature-induced phase transformation reverses deformation...Typically the martensitic (low-temperature) phase is monoclinic or orthorhombic . Since these crystal structures do not have enough slip systems for easy dislocation motion, they deform by twinning—or rather, detwinning.

Martensite is thermodynamically favored at lower temperatures, while austenite (B2 cubic) is thermodynamically favored at higher temperatures. Since these structures have different lattice sizes and symmetry, cooling austenite into martensite introduces internal strain energy in the martensitic phase. To reduce this energy, the martensitic phase forms many twins—this is called "self-accommodating twinning" and is the twinning version of geometrically necessary dislocations. 

In different words, I think the essential idea may be the following. In most metals large strains are accomodated by topological defects such as dislocations. These become entangled leading to work hardening and irreversible changes is macroscopic shapes. Shape memory alloys are different because of the low symmetry unit cell. The most natural defects are twinning domain walls and they are not topological and so their formation is reversible.

I am looking forward to reading the book chapter Shape memory alloys by Vladimir Buljak, Gianluca Ranzi

Another fascinating phenomena that is related to shape-memory is "superelasticity", which I discussed in an earlier post on organic molecular crystals, and has recently been reviewed.

I welcome clarification  of the essential physics.

An emergentist perspective on public policy issues that divide

How is the whole related to the parts?

Which type of economy will produce the best outcomes: laissez-faire or regulated?

Can a government end an economic recession by "stimulus" spending?  

What is the relative importance of individual agency and social structures in causing social problems such as poverty and racism?

These questions are all related to the first one. Let's look at it from an emergentist perspective, with reference to physics. 

Consider the Ising model in two or more dimensions. The presence of nearest neighbour interactions between spins leads to emergent properties: long-range ordering of the spins, spontaneous symmetry breaking below the critical temperature, and singularities in the temperature dependence of thermodynamic properties such as the specific heat and magnetic susceptibility. Individual uncoupled spins have neither property. Even a finite number of spins do not. (Although, a large number of spins do exhibit suggestive properties such as an enhancement of the magnetic susceptibility near the critical temperature). Thus, the whole system has properties that are qualitatively different from the parts. 

On the other hand, the properties of the parts, such as how strongly the spins couple to an external field and interact with their neighbours, influence the properties of the whole. Some details of the parts matter. Other details don't matter. Adding some interaction with spins beyond nearest neighbours does not change any of the qualitative properties, provided those longer-range interactions are not too large. On the other hand, changing from a two-dimensional rectangular lattice to a linear chain removes the ordered state. Changing to a triangular lattice with an antiferromagnetic nearest-neighbour interaction removes the ordering and there are multiple ground states. Thus, some microscopic details do matter.

For illustrative purposes, below I show a sketch of the temperature dependence of the magnetic susceptibility of the Ising model for three cases: non-interacting spins (J=0), two dimensions (d=2), and one dimension (d=1). This shows how interactions can significantly enhance/diminish the susceptibility depending on the parameter regime.

The main point of this example is to show that to understand a large complex system we have to keep both the parts and the whole in mind. In other words, we need both microscopic and macroscopic pictures. There are two horizons, the parts and the whole, the near and the far. There is a dialectic tension between these two horizons. It is not either/or but both/and.

I now illustrate how this type of tension matters in economics and sociology, and the implications for public policy. If you are (understandably) concerned about whether Ising models have anything to do with sociology and economics, see my earlier posts about these issues. The first post introduced discrete-choice models that are essentially Ising models. A second post discussed how these show how equilibrium may never be reached leading to the insight that local initiatives can "nucleate" desired outcomes. A third post, considered how heterogeneity can lead to qualitative changes including hysteresis so that the effectiveness of "nudges" can vary significantly.

A fundamental (and much debated) question in sociology is the relationship between individual agency and social structures. Which determines which? Do individuals make choices that then lead to particular social structures? Or do social structures constrain what choices individuals make. In sociology, this is referred to as the debate between voluntarism and determinism. A middle way, that does not preference agency or structure, is structuration, proposed by Anthony Giddens.

Social theorists who give primacy to social structures will naturally advocate solving social problems with large government schemes and policies that seek to change the structures. On the other side, those who give primacy to individual agency are sceptical of such approaches, and consider progress can only occur through individuals, and small units such as families and communities make better choices. The structure/agency divide naturally maps onto political divisions of left versus right, liberal versus conservative, and the extremes of communist and libertarian. An emergentist perspective is balanced, affirming the importance of both structure and agency.

Key concepts in economics are equilibrium, division of labour, price, and demand. These are the outcomes of many interacting agents (individuals, companies, institutions, and government). Economies tend to self-organise. This is the "invisible hand" of Adam Smith. Thus, emergence is one of the most important concepts in economics. 

A big question is how the equilibrium state and the values of the associated state variables (e.g., prices, demand, division of labour, and wealth distribution) emerge from the interactions of the agents. In other words, what is the relationship between microeconomics and macroeconomics?

What are the implications for public policy? What will lead to the best outcomes (usually assumed to be economic growth and prosperity for "all")? Central planning (or at least some government regulation) is pitted against laissez-faire. For reasons, similar to the Ising and sociology cases, an emergentist perspective is that the whole and the parts are inseparable. This is why there is no consensus on the answers to specific questions such as, can government stimulus spending move an economy out of a recession? Keynes claimed it could but the debate rages on.

An emergentist perspective tempers expectations about the impact of agency, both individuals and government. It is hard to predict how a complex system with emergent properties will respond to perturbations such as changes in government policy. This is the "law" of unintended consequences.

“The curious task of economics is to demonstrate to men how little they really know about what they imagine they can design.”

Friedrich A. Hayek, The Fatal Conceit: The Errors of Socialism

I think this cuts both ways. This is also reason to be skeptical about those (such as Hayek's disciples) who think they can "design" a better society by just letting the market run free.

Diversity is a common characteristic of emergent properties

Consider a system composed of many interacting parts. I take the defining characteristic of an emergent property is novelty. That is, the whole has a property not possessed by the parts alone. I argue that there are five other characteristics of emergent properties. These characteristics are common but they are neither necessary nor sufficient for novelty.

1. Discontinuities

2. Unpredictability

3. Universality

4. Irreducibility

5. Modification of parts and their relations

I now add another characteristic.

6. Diversity

Although a system may be composed of only a small number of different components and interactions, the large number of possible emergent states that the system can take is amazing. Every snowflake is different. Water is found in 18 distinct solid states. All proteins are composed of linear chains of 20 different amino acids. Yet in the human body there are more than 100,000 different proteins and all perform specific biochemical functions. We encounter an incredible diversity of human personalities, cultures, and languages. 

A related idea is that "simple models can describe complex behaviour". Here "complex" is often taken to mean diverse. Examples, how simple Ising models with a few competing interactions can describe a devil's staircase of states or the multitude of atomic orderings found in binary alloys.

Perhaps the most stunning case of diversity is life on earth. Billions of different plant and animal species are all an expression of different linear combinations of the four base pairs of DNA: A, G, T, and C.

One might argue that this diversity is just a result of combinatorics. For example, if one considers a chain of just ten amino acids there are 10^13 different possible linear sequences. But this does not mean that all these sequences will produce a functional protein, i.e., one that will fold rapidly (one the timescale of milliseconds) into a stable tertiary structure, and one that can perform a useful biochemical function. 

Condensed matter physics in 15 minutes!

Oxford University Press has a nice podcast on Very Short Introductions. 

In each episode, an author of a specific volume has 10-15 minutes to introduce themself and answer several questions.

What is X [the subject of the VSI]?

What got you first interested in X?

What are the key aspects of X that you would like everyone to know?

The ones I have listened to and particularly liked are Infinity, Philosophy of Science, Evangelicalism, Development, Consciousness, Behavioural Economics, and Modern China.

Tomorrow, I am recording an episode for Condensed Matter Physics: A Very Short Introduction.

Here is a practise version of the audio and the draft text is below. 

I welcome feedback.

VSI Podcast 

I am Ross McKenzie. I am an Emeritus professor of physics at the University of Queensland in Brisbane, Australia. I have spent the past forty years learning, teaching, and researching condensed matter physics. I really love the Very Short Introduction series and so I am delighted to share my experience by writing Condensed Matter Physics: A Very Short Introduction.

What is condensed matter physics? It is all about states of matter. At school, you were probably taught that there are only three states of matter: solid, liquid, and gas. This is wrong. There are many more states such as liquid crystal, glass, superconductor, ferromagnet, and superfluid. New states of matter are continually, and often unexpectedly, being discovered. Condensed matter physics investigates how the distinct physical properties of states of matter emerge from the atoms of which a material is composed.

What first got me interested in condensed matter physics?

After I finished an undergraduate degree in theoretical physics in Australia in 1982, I would not have been able to answer the question, “what is condensed matter physics?”, even though it is the largest sub-field of physics. I then went to Princeton University in the USA to pursue a Ph.D. in and I took an exciting course on the subject and began to interact with students and faculty working in the field. 

At Princeton was Phil Anderson, who had won a Nobel Prize in physics for work in condensed matter. At the time I did not appreciate his much broader intellectual legacy. In his recent biography of Anderson, Andrew Zangwill states “more than any other twentieth-century physicist, he [Anderson] transformed the patchwork of ideas and techniques formerly called solid-state physics into the deep, subtle, and intellectually coherent discipline known today as condensed matter physics.” Several decades later, my work became richer as Anderson gave me an appreciation of the broader scientific and philosophical significance of condensed matter physics, particularly its connection to other sciences, such as biology, economics, and computer science. When do quantitative differences become qualitative differences? Can simple models describe rich and complex behaviour? What is the relationship between the particular and the universal? How is the abstract related to the concrete?

So what are the key aspects of condensed matter physics that I would like everyone to know?

First, there are many different states of matter. It is not just solid, liquid, and gas. Consider the “liquid crystals” that are the basis of LCDs (Liquid Crystal Displays) in the screens of televisions, computers, and smartphones. How can something be both a liquid and a crystal? A liquid crystal is a distinct state of matter. Solids can be found in many different states. In everyday life, ice means simply solid water. But there are in fact eighteen different solid states of water, depending on the temperature of the water and the pressure that is applied to the ice. In each of these eighteen states, there is a unique spatial arrangement of the water molecules and there are qualitative differences in the physical properties of the different solid states.

Condensed matter physics is concerned with characterising and understanding all the different states of matter that can exist. These different states are called condensed states of matter. The word “condensed’’ is used here in the same sense as when we say that steam condenses into liquid water. Generally, as the temperature is lowered or the pressure is increased, a material can condense into a new state of matter. Qualitative differences distinguish the many different states of matter. These differences are associated with differences in symmetry and ordering.

Second, condensed matter physics involves a particular approach to understanding properties of materials. Every day we encounter a diversity of materials: liquids, glass, ceramics, metals, crystals, magnets, plastics, semiconductors, and foams. These materials look and feel different from one another. Their physical properties vary significantly: are they soft and squishy or hard and rigid? Shiny, black, or colourful? Do they absorb heat easily? Do they conduct electricity? The distinct physical properties of different materials are central to their use in technologies around us: smartphones, alloys, semiconductor chips, computer memories, cooking pots, magnets in MRI machines, LEDs in solid-state lighting, and fibre optic cables. Why do different materials have different physical properties? 

Materials are studied by physicists, chemists, and engineers, and the questions, focus, goals, and techniques of researchers from these different disciplines can be quite different. The focus of condensed matter physics is on states of matter. Condensed matter physics as a research field 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. The aim is to address fundamental questions and to find unifying concepts and organizing principles to understand a wide range of phenomena in materials that are chemically and structurally diverse. 

The central question of condensed matter physics is, how do the properties of a state of matter emerge from the properties of the atoms in the material and their interactions? 

Let’s consider a concrete example, that of graphite and diamond. While you will find very cheap graphite in lead pencils, you will find diamonds in jewelery. Both graphite and diamond are composed solely of carbon atoms. They are both solid. So why do they look and feel so different?  Graphite is common, black, soft, and conducts electricity moderately well. In contrast, diamond is rare, transparent, hard, and conducts electricity very poorly. We can zoom in down to the scale of individual atoms using X-rays and find the spatial arrangement of the carbon atoms relative to one another. These arrangements are qualitatively different in diamond and graphite.. Diamond and graphite are distinct solid states of carbon. They have qualitatively different physical properties, at both the microscopic and the macroscopic scale. 

Third, I want you to know about superconductivity, one of the most fascinating states of matter. I have worked on it many times over the past forty years. Superconductivity occurs in many metals when they are cooled down to extremely low temperatures, close to absolute zero (-273 ºC). In the superconducting state, a metal can conduct electricity perfectly; without generating any heat. This state also expels magnetic fields meaning one can levitate objects, whether sumo wrestlers or trains. 

The discovery of superconductivity in 1911 presented a considerable intellectual challenge: what is the origin of this new state of matter? How do the electrons in the metal interact with one another to produce superconductivity? Many of the greatest theoretical physicists of the twentieth century took up this challenge but failed. The theoretical puzzle was only solved 46 years after the experimental discovery. The theory turns out also to be relevant to liquid helium, nuclear physics, neutron stars, and the Higgs boson. New superconducting materials and different superconducting states continue to be discovered. A “holy grail” is to find a material that can superconduct at room temperature. 

I find superconductivity even more interesting when considering quantum effects. By 1930 it was widely accepted that quantum theory, in all its strangeness, describes the atomic world of electrons, protons, and photons. However, this strangeness does not show itself in the everyday world of what we can see and touch. You cannot be in two places at the same time. Your cat is either dead or alive. However, condensed matter physicists have shown that the boundary between the atomic and macroscopic worlds is not so clear cut. A piece of superconducting metal can take on weird quantum properties, just like a single atom, even though the metal is made of billions of billions of atoms. It is in two states at the same time, almost like Schrodinger’s famous cat.

Fourth, condensed matter physics is all about emergence; the whole is greater than the sum of the parts. A system composed of many interacting parts can have properties that are qualitatively different from the properties of the individual parts. Water is wet, but a single water molecule is not. Your brain is conscious, but a single neuron is not. Such emergent phenomena occur in many fields, from biology to computer science to sociology, leading to rich intellectual connections. Condensed matter physics is arguably the field with the greatest success at understanding emergent phenomena in complex systems, particularly at the quantitative level. This is not because condensed matter physicists are smarter than sociologists, economists, or neuroscientists. It is because the materials we study are much “simpler” than societies, economies, and brains. 

Finally, condensed matter physics is one of the largest and most vibrant sub-fields of physics. For example, in the past thirty years, the Nobel Prize in Physics has been awarded thirteen times for work on condensed matter. In the past twenty years, eight condensed matter physicists have received the Nobel Prize in Chemistry. 

I hope I have sparked your interest in condensed matter physics. I invite you to learn more about why I consider this field of science significant, beautiful, and profound. 

Opening the door for women in science

 I really liked reading Transcendent Kingdom by Yaa Gyasi. She is an amazing writer. I recently reread some of it for an extended family book club. Just check out some of these quotes. 

A colleague suggested I might like Lessons in Chemistry, a novel by Bonnie Garmus. I have not read the book yet, but I have watched the first two episodes of the TV version on AppleTV. I watched the first episode for free.

The show contains a good mix of humour, love of science, and feminism. The chemistry dialogue seems to be correct. The show chronicles just how in the 1950s how awful life was for a young woman who aspired to be a scientist. Things have improved. But there is still a long way to go...