Monday, March 4, 2019

Ten key ideas about condensed matter physics?

I am slowly working towards writing a Condensed Matter Physics: Very Short Introduction.
But first I am trying to clarify my audience and goals. Some earlier posts have helped me clarify this.

My intended audience is probably not you! Rather it is a person who wants to get the flavour of what CMP is actually about.  Examples might include a smart final year high school who wants to study science at university, or a first-year chemistry undergraduate, or an economics graduate, or a sociology professor, ...

My goal is to show that CMP is intellectually exciting, intellectually challenging, and intellectually important.

The VSI format is 8-10 chapters and 30-35 thousand words. It is meant to be written in the style of an engaging essay not a technical paper.

My plan is to basically have one clear and specific idea that I want to communicate in each chapter. I am thinking that in order to increase interest and comprehension that for each chapter I will aim to include.

An easily understandable analogy to illustrate the main idea.
A few relevant and illuminating figures.
An interesting historical anecdote.
An example of a technological application.
An example of cross-fertilisation to another field of science.

So here is the current version of my chapter headings and the main idea(s) I want each chapter to communicate.

1.     What is condensed matter physics?

CMP is concerned with studying and understanding material systems composed of large numbers of atoms. How do the properties of the system emerge from the properties of the constituent atoms and the interactions between them? It is a multi-faceted approach to studying materials and involves a unifying set of concepts. Quite abstract ideas and concepts can be quite powerful for understanding quite practical systems.

2.     A plethora of states of matter

Even for the simplest materials, there is a multitude of different phases, i.e. qualitatively different states of matter. Transitions between distinct phases are defined by discontinuities in properties. Phase diagrams encode what phase is stable under specific external conditions such as temperature, pressure, and magnetic field.

3.     Symmetry matters

Distinct phases are associated with distinct ordering of the system. A unifying concept to distinguish and classify different phases and their associated ordering is how they differ in the type of symmetry that they have. What different classes of symmetry are mathematically possible significantly constrains what is physically possible.

4.     The order of things

The type and quantity of order and the broken symmetry in a distinct state of matter can be described by a small set of numbers represented by the “order parameter’’.

5.     Adventures in flatland

Confining a material to one or two dimensions can lead to new states of matter. Furthermore, imagining a world of variable dimension can actually lead to a better understanding of materials in our three-dimensional world.

6.     The critical point: details do not matter

Under a very special set of external conditions, a phase transition is not associated with discontinuous properties. These conditions are represented by the critical point in the phase diagram.  Very different material systems can have the same properties close to the critical point. Understanding this universality requires looking at the system at many different length scales.

7.     Quantum matter

The weirdness of quantum theory is most commonly manifest at the level of single atoms and molecules. Surprisingly, quantum effects can also be seen “with the naked eye” in states of matter such as superconductors and superfluids.

8.     Topology matters

Abstract ideas about shapes help us understand spatially non-uniform broken symmetry states. They also lead to new states of quantum matter, that do not involve broken symmetry.

9.     Emergence matters

Condensed matter physics is all about emergence: the sum is greater than the parts. From a system composed of many interacting components new (often unanticipated) properties, concepts, and organising principles emerge. Reality is stratified.

10.  Future challenges

Almost all new states of matter are discovered by experiment and often by accident rather than being predicted theoretical. An open question and challenge is to what extent one can predict new states or to design materials with specific properties. There are significant open challenges in all facets of CMP: synthesis, characterisation, measurement, computation, and theory. Finally, given the great success of CMP at understanding emergence in complex systems a challenge is to adapt the approach and concepts to other complex systems, ranging from biology to sociology.

I welcome feedback.
But keep in mind the audience.
I do not want to add material, but perhaps even cut material (e.g. chapter 8).

What do you wish non-CMP people understood about CMP?


  1. Hi Prof. Ross

    Perhaps you can add a brief comment on the non-equilibrium aspects of the CMP, the importance in the emergency and the challenges in the current research in this area. For example the biological systems are far from equilibrium and needs new tools and ideas and maybe will lead the future of the theoretical physics. However I know the topic can be a quite technical for a lay audience.

  2. I think its in condensed matter physics that the idea of "effective theories" is most powerful and its not just in the critical phenomena limit of large correlation lengths. They tell you the starting point for a calculation, often from an unexpected point of view. To some extent this is Landau theory all over again, but it doesn't need to be in the sense of an expansion of a free energy in an order parameter. I'm thinking of paradigmatic models of non-equilibrium surface growth (KPZ - a postulated equation), a model Hamiltonian for membrane shapes and fluctuations (Helfrich and others - a postulated form for the energy of a curved membrane), powerful conjectures for quantum wave-functions of interacting systems in the high B limit (Laughlin, Jain and others - a guessed wave function), any amount of work by de Gennes in taking an incredibly complicated problem and extracting just the right ingredients to make an effective model.

  3. WoW! These 10 prime ideas was really amazing. Because Physics are important of science. Just you wrote amazing.
    Thanks for it and here is the NU Honours 4th Year Routine. You can check it.