Instructor: Nigel Goldenfeld

Time: 2.00-3.20pm, Mondays and Wednesdays

Place: Loomis Lab 136

Nigel's office hour will be Mondays at 4-5 pm in ESB 3-113.

**Please register for the email list for the class, so that last minute announcements, class cancellations etc. can be sent to you.**

Course gradebook for the full course.

Lecture notes for the course are available online. A list of typos can be found here; please add to it if you find any.

Graders:

**Oleg Dubinkin** (olegd2@illinois.edu) will have office hour in 390J at Thur 4-5.

**Ben Strekha** (strekha2@illinois.edu) will have office hour at Fri 4-5.

Ben's office hours will take place in the "open area" on the third floor connecting corridor between ESB and MRL, and Oleg may have the option to utilize that space if his office is too small.

**2018 Spring Term Essays are here. **

Other than that ... Nothing to see here. Move along or watch a movie.

**Handouts and Assignments**

Course details

Revision of 2nd Quantisation

**Tentative syllabus**.

- Emergent states and long-range order

Introduction to emergent states; long-range order; continuous symmetries - Off-diagonal long-range order

Bose-Einstein condensation; topological excitations; quasi-particles - General theory of spontaneous symmetry breaking

Goldstone's theorem; response functions; excitations; emergent properties; Landau theory; generalized elasticity theory - Pairing in superconductors and nuclear matter

Ginzburg-Landau theory; BCS theory; QCD - Liquid crystals

Nematics and smectics; analogue with superconductivity - Emergence in complex biological systems

Networks and self-organisation - Emergent states far from equilibrium

Rayleigh-Benard convection; bifurcations; Landau theory and generalized elasticity theory far from equilibrium

**Emergent states of matter movie page**

Superfluid flow phenomena can be visualized with some ingenuity, and I have assembled some resources related to superfluidity on the emergent states of matter movie page. In the future, I may add other material to this page.

**Recommended books **

I have not yet written a textbook for this course which covers all the material in the way I teach it. However, past students in this course have found that the books below are useful supplements to my class notes.

**(A) General references on spontaneous symmetry breaking, Landau theory and generalized elasticity theory.**

P. Chaikin and T. Lubensky. *Principles of Condensed Matter Physics*.

N. Goldenfeld. *Lectures on Phase Transitions and the Renormalization Group*.

L.H. Ryder. *Quantum Field Theory*. There is no quantum field theory per se in the course, but some students liked the discussion of symmetry breaking in this book.

A. Altland and Ben Simons. *Condensed Matter Field Theory.* This is an advanced book, but one of the best to learn about the modern approach to condensed matter theory, with many-body theory done by functional integral techniques, and a clear and readable presentation of many technical issues.

Mehran Kardar. *Statistical Physics of Fields*. A clear and well-written introduction to modern ways to deal with collective phenomena in condensed matter physics.

**(B) Off-diagonal long-range order and condensates**

J. Annett. *Superconductivity, Superfluids and Condensates*.

C.J. Pethick and H. Smith. *Bose-Einstein Condensation in Dilute Gases*

**(C) Superconductivity**

M. Tinkham. *Introduction to Superconductivity*.

**(D) Liquid Crystals**

P.G. de Gennes. *The Physics of Liquid Crystals*.

**(E) Quantum Hall Effects**

M. Stone. *The Quantum Hall Effect.*

**(F) Biological emergence**

S. Strogatz. *Sync*

C. R. Woese. *On the evolution of cells*, Proc. Natl. Acad. Sci. USA 99, 8742-7 (2002).

**(G) Pattern Formation**

M. Cross and P. Hohenberg. *Pattern Formation Outside of Equilibrium*, Reviews of Modern Physics 65, 851-1112 (1993).

Complexity and emergent phenomena are very much frontier topics across disciplines of science. As an example, here is a report recently issued by the US Department of Energy on the importance of this topic.

*Data *

Here is a
set of real experimental data on the penetration depth of the high temperature
superconductor YBCO, which were published
in S. Kamal, D. Bonn, N. D. Goldenfeld, Hirschfeld, R. Liang and W. N. Hardy. Penetration
depth measurements of 3D XY critical behaviour in YBa2Cu3O6.95 crystals. Phys. Rev. Lett. *73*,
1845-1848 (1994).

2018 Fall Term Essays are here.

2012 Fall Term Essays are here

2011 Fall Term Essays are here

2010 Fall Term Essays are here

2009 Fall Term Essays are here

2008 Fall Term Essays are here

2007 Fall Term Essays are here

2006 Fall Term Essays are here

2006 Spring Term Essays are here

2004 Fall Term essays are here.

2004 Spring Term essays are here.

2002 Term essays are here.

Instead of a final exam, this course will have a term paper assignment. The subject matter can be any topic in physics which is related to Emergent States of Matter in some sense. Since many interesting phenomena are a manifestation of spontaneous symmetry breaking, you have unusual latitude in your choice of topic. It need not be restricted to condensed matter but can cover the many recent and exciting developments in other areas of science, including, but not limited, to: high energy physics, cosmology, even biology. I hope many of you will chose topics in these non-condensed matter areas.

Your essay should not duplicate an essay that you have written for another course, nor should it duplicate your research work. The purpose is to give you something fresh to write about, related to the topic of the course.

I can provide you with a guide to the literature for many topics if you come and ask me. However, I really don't want to do this. Part of this assignment is to give you an opportunity to develop the skills in doing a literature survey and digging up information from the library. Other important components of this assignment are that you demonstrate good taste, curiosity and ambition in your choice of subject, and that you are capable of distilling the most important and essential details from very technical papers.

Some hints: look at the back of
the current *Reviews of Modern Physics* where you will find a listing of topics that
have been reviewed in the last ten years or so. These are always a good starting point.
Similarly for journals such as *Advances in Physics* and *Reports of Progress in
Physics*. Use internet keyword searches on http://xxx.lanl.gov
archives and search engines such as Google.

Don't be restricted by the topics that we addressed in class. We didn't have time to cover the huge variety of emergent states of matter that arise in the real world. Here is a partial list of subject areas to prompt your thinking:

*Exotic superfluidity*

Superfluid phenomena in Helium 3

Superfluid phenomena in neutron stars

Superfluid phenomena in nuclei

*Exotic superconductivity*

Heavy fermion superconductors

Unconventional pairing states in cuprate superconductors

Unconventional pairing states in non-cuprate superconductors

Fluctuation effects in superconductors

Vortex liquids, glasses and other aspects of the magnetic phase diagram of the cuprates

*Liquid crystals*

Analogies between liquid crystals and superconductors

Smectic phases in liquid crystals

Dynamics of topological defects in liquid crystals

Phase transition kinetics in liquid crystals

Blue phases

*Emergent states of matter*

Ordered phases in optical lattices (superfluid, Mott insulators, ...)

Quantum hall states of rapidly rotating BECs

Magnetic states of condensed matter (ferromagnets, antiferromagnets, spin glass, ...)

Disordered states of matter (Griffiths phases, random field Ising models, localization, ...)

*High energy physics*

Phases of quantum chromodynamics

Recent experimental puzzles from RHIC

Quark-gluon plasma and its dynamics

*Cosmology*

The electroweak phase transition in the early universe and its consequences

Cosmological manifestations of strings and other topological defects

Space-time as an emergent phenomenon

Phase transitions and inflationary cosmology

*Nonequilibrium systems*

Collective behaviour in animals (herding, flocking, schooling, ...)

Traffic flow (shocks, phase diagram, pedestrians ...)

Reaction-diffusion patterns

Convection effects in fluids

Bioconvection

Emergence of network properties (WWW, metabolic networks, ...)

Evolution

Synchronisation of coupled oscillators

**Detailed Directions**

The purpose of your essay is to explain why the problem is interesting, what has been done, and what are the conclusions. Don't go into unnecessary technical details. The amount that you personally chose to work through the technical details is up to you; my goal is that you understand the broad issues. Hopefully you will find your topic sufficiently interesting that you will wish to delve deeper (and perhaps even think for yourself about the subject). You should imagine that you are writing the paper for a reader who is like you were before you started thinking about your topic. Every essay must include some sort of discussion of experiment or observations: these can either be the focus of the essay, or at least must be mentioned specifically with regard to how they demonstrate, provide counter-examples to, or otherwise inform theory. Essays which are purely theoretical will receive a relatively lower grade than others. More detailed suggestions about format are given below.

The final exam/paper is due by **8:00-11:00 a.m., Thursday, May 10 2018**. **No excuses for lateness will be accepted** unless there are
extenuating circumstances or previous arrangements have been made, in accord with
University regulations. It should be no more than 12 pages long, single spaced 12
point font, including figures and references (include some up-to-date review articles, and try to limit the references to around 10 or so). I will not read more than 12 pages of an essay. Essays are graded for effort, so if it is significantly shorter than 12 pages, it is likely that you will lose credit also. You
have been warned! In addition to the 12 pages of the essay, there should be a cover page, which will consist of the following (a) Title, (b)
author's name, (c) abstract.

Your essay must be written in an electronic format, including the figures, if any. Ultimately, all essays will be posted on the WWW. The format for submission will ONLY be an Acrobat PDF file.

**Submission instructions:**

(A) Write your essay in TeX, Word, whatever, ... and then convert it to a PDF file. There are plenty of free tools to do that.

(B) Name your essay according to the following scheme

<Your last name>.pdf

(Example: goldenfeld.pdf)

(C) Email to Nigel Goldenfeld <nigel@uiuc.edu>

Make the subject heading of your email

569 ESM <Your last name>.pdf

and have in the body of the email your name, the title and a brief abstract of your essay.

**EXAMPLE**

************************************************************

To: nigel@uiuc.edu

From: smith@uiuc.edu

Subject: 569 ESM smith.pdf

-------------------------------------

Author: Freda Smith

Title: Critical dynamics of the superconducting transition

Abstract:

This essay describes the observations, computer simulations, and analytic theory of critical fluctuation contributions to the electrical and thermal conductivity near the superconducting transition of the high temperature superconductors YBCO and BSCCO.

***********************************************************

**Format: **

Your paper should have approximately the following structure, but feel free to modify it to fit your chosen topic. Here are some suggestions for the sorts of questions your paper should address to make it most useful to the reader. As you will see, the purpose is not to focus too much on technical details.

**Introduction and Background:**

What hypotheses are being tested in this paper?

What information induced the authors to perform the experiments/theory?

What new methods or insights brought to bear on the problem?

Why did you chose to write about this topic?

Why is this interesting or important?

**Methods:**

What are the critical methods of the paper?

What enabling technologies are used?

What are the weaknesses of the methods used?

Are there other or better approaches that could be used?

**Results and Discussion**

What are the primary conclusions of the paper?

Did the authors prove their hypotheses?

What novel information or directions come from this work?

What control experiments were performed? (If appropriate)

What assumptions still remain in the work?

How could these assumptions be tested?

What other explanations for the observations are still possible?

What would you do next to advance this field?

- Useful
resource: don't forget the valuable series of top-flight review articles on
superconductivity which are in the series of books edited by Parks.

- Link to recent papers on the statistical mechanics section of the condensed matter preprint archive at Los Alamos. Note that many, many papers relevant to statistical mechanics and phase transition physics are not listed here, but appear in the condensed matter section.

*Nigel Goldenfeld*

- Telephone: (217)-333-8027

Office: 3113 ESB

Office hour: Mon 4pm-5pm or by appointment - Nigel Goldenfeld's Home Page

Updated: Jan 16 2018