Last Modified: April 30, 2002

Homework #5: [PDF] [PostScript]. Due date: 04/25/2002 by 6 p.m.

Homework #4: [PDF] [PostScript]. Due date: 04/16/2002 by 6 p.m.

Homework #4 Solutions: [Problem I.1][Problem I.2][Problem I.3][Problem I.4][Problem I.5]

Midterm: [PDF] [PostScript]. Due date: 04/04/2002 by 12 p.m. or by 6 p.m. for 0.5 of grade.

Homework #4 Solutions [PDF][PostScript]

Homework #3: [PDF] [PostScript]. Due date: 04/02/2002 by 6 p.m.

Homework #3 Solutions: [Problem I.1][Problem I.2][your favourite textbook][Problem I.4][Problem I.5][Problem I.6][Bonus Problem]

Homework #2: [PDF] [PostScript]. Due date: 03/19/2002 by 6 p.m.

Homework #2 Solutions: [Problem I.1][Problem I.2][Problem I.3][Problem I.4][Problem I.5][Problem I.6][Bonus Problems]

Homework #1: [PDF] [PostScript]. Due date: 03/04/2002 by 10 a.m.

Homework #1 Solutions: [Section I][Section II][Problem III.1][Problem III.2][Problem III.3][Problem III.4][Problem III.5][Problem III.6][Problem III.7][Problem III.8][Problem III.9]

Example 1 may help you to do homework #1.

Homework #0: explore this

Statistical Mechanics I: Project Paper Instructions

Before you start working on a project, send me an e-mail stating the topic and name(s) of author(s) for approval. Please, do it before April 5, 2002.

[download this text in PDF format]

The subject matter can be any topic in physics which is related to Statistical Physics in some sense. Since many interesting phenomena involve many-particle systems, you have unusual latitude in your choice of topic. It need not be restricted to “pure” statistical mechanics 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 you will chose topics in these non-canonical areas. Also, I have no objection to people choosing to write about their own research area (past, present, or future) if it falls within the scope of the course. I provide a list of some of topics, including the literature, near the end of this document. You can choose one of those, and use the literature list as a starting point. However, I generally want you go beyond that. 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 and the Internet. Other important components of this assignment are that you demonstrate 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 to find an interesting topic. 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.

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. I strongly prefer that 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 counterexamples to, or otherwise inform theory.

More detailed suggestions about format (suggestions for the sorts of questions your paper should address to make it most useful to the reader):

q       What hypotheses are being tested in this paper?

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

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

q       Why did you chose to write about this topic?

q       Why is this interesting or important?

q       What are the weaknesses of the methods used?

q       Are there other or better approaches that could be used?

q       What are the primary conclusions of the paper?

q       What novel information or directions come from this work?

q       What assumptions still remain in the work?

q       How could these assumptions be tested?

q       What other explanations for the observations are still possible?

q       What would you do next to advance this field?

Remember: you are allowed to work on projects either individually or in groups up to three people. In the latter case you must note of your collaborators (just as if you were writing a scientific paper). However, each project must be written up individually.

Cheating (I do not like to talk about this, but…): University policy states that cheating is a scholastic offence. Moreover, simply do not jeopardize your career in this School by cheating. I anticipate no problems in this regard, but still you may be required to submit your term paper to http://www.turnitin.com.

The paper is due by noon Mon April 29, 2002.

Submission before the deadline will insure that I have time to read the essay and make adjustments to your final grades. The paper must be 8 to 12 pages long, single spaced 12 point font, including figures and the list of references. I will not read more than 12 pages of an essay. You have been warned!

Your essay must be written in an electronic format, including the figures, if any. Figures may be scanned, captured electronically using screen capture programs, or generated electronically: hard copy can be scanned in if necessary using the scanner in my laboratory. With your permission, I would like to ultimately post essays on the WWW. The format for submission will ONLY be an Acrobat PDF file or gzipped PostScript file. For those of you using MS Word, I can convert a Word file into PDF, but you must give me a day in advance of the due date to do that, please.

Each essay should include a cover page which will consist of the following:

(a) Title and author's name,

(b) abstract.

The essays should also have a decent set of references, which should include particularly good review articles.

Submission instructions:

q       Name your essay according to the following scheme: <Your_last_name your_first_name 6107 2002>.pdf (Example: Marchenkov Alexei.pdf)

q       Email to Alexei Marchenkov (alexei.marchenkov@physics.gatech.edu)

q       Make the subject heading of your email: 6107 Project;  and have in the body of the email your name, the title and a brief abstract of your essay.

EXAMPLE

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

To: alexei.marchenkov@physics.gatech.edu

From: gt*@*.gatech.edu

Subject: 6107 Project

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

Author: Bart Simpson

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.

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

GOOD LUCK AND HAVE FUN!

List of recommended topics.

 The Statistical Mechanics of polymers.

q       P. G. deGennes, ``Scaling Concepts in Polymer Physics", Cornell University Press (1980)

q       S. F. Edwards, Proc. Phys. Soc. 85, 613 (1965)

Statistical Mechanics of Liquid Crystals

q       P.G. de Gennes and J. Prost, "The Physics of Liquid Crystals", Chapters 1,2 and 10.

q       P.M. Chaikin & T.C. Lubensky, "Principles of Condensed Matter Physics", Chapter 6.

Kosterlitz-Thouless theory in two-dimensional superfluids, melting and spin systems.

q       J. M. Kosterlitz and D.J. Thouless, J. Phys. C6, 1181 (1973)

q       J.V. Jose, L.P. Kadanoff, S. Kirkpatrick and D.R. Nelson, Phys. Rev. B 16, 1217 (1977)

q       D. R. Nelson and B. I. Halperin, Phys. Rev. B 19, 2457 (1979)

The superfluid transition in helium

q       R. P. Feynman, "Statistical Mechanics", W. Benjamin, 1973, Chapter 11.

Non-Equilibrium Statistical Mechanics: Large Deviation Theory

q       Y. Oono, Prog. Theor. Phys. Supp. 99, 165-205 (1989).

Percolation

q       D.Stauffer and A. Aharony, "Introduction to Percolation Theory", Taylor & Francis, 1992.

q       F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982).

Lattice Gauge Theories and Phase transitions

q       J.B. Kogut, Rev. Mod. Phys. 51, 659 (1979).

Theory of Spin Glasses

q       S.F. Edwards and P. W. Anderson, J. Phys. F 5, 965 (1975); J. Phys. F 6, 1927 (1975).

q       D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).

q       K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986).

Renormalization Group approach to Spin Systems

q       L.P. Kadanoff, "Statistical Physics: Statistics, Dynamics and Renormalization", World Scientific, 2000, Chapters 13 and 14 and references therein.

The physics of the quark-gluon plasma

q       Larry McLerran , Rev. Mod. Phys. 58, 1021 (1986)

The renormalization group in the theory of critical behavior

q       M. E. Fisher, Rev. Mod. Phys. 46, 597 (1974)

Duality Transformations in Statistical Mechanics

q       H. Kramers and G. Wannier, Phys. Rev. 60, 252 (1941)

q       R. Savit, Rev. Mod. Phys. 52, 453 (1980)

q       L.P. Kadanoff, "Statistical Physics: Statistics, Dynamics and Renormalization", World Scientific, 2000, Chapter 15. 

Quantum Phase Transitions

q       J.A. Hertz, Phys. Rev. B. 14, 1165 (1976)

q       Subir Sachdev, "Quantum Phase Transitions" Cambridge University Press, 2001.

Dynamics of Earthquake Faults

q       J. M. Carlson, J. S. Langer, and B. E. Shaw, Rev. Mod. Phys. 66, 657-670 (1994)

Critical Dynamics of continuous phase transitions:

q       P.C. Hohenberg and B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977).

Phase Transitions in Quantum Field Theory

q       J.I. Kapusta, "Finite-temperature Field Theory", Cambridge Univ. Press, 1989.

Brain, neural networks, and computation

q       D. Amit, "Modeling Brain Function", Cambridege University Press, 1989

q       J. J. Hopfield, Rev. Mod. Phys.71S, 431 (1999)

Modeling molecular motors

q       F. Jülicher, A. Ajdari, and J. Prost Rev. Mod. Phys. 69, 1269-1282 (1997)

The Statistical Physics of Money

q       Jean-Philippe Bouchaud and Marc Potters, "Theory of Financial Risks: From Statistical Physics to Risk Management", Cambridge University Press (2000).

q       J.-P. Bouchaud and D. Sornette, "The Black-Scholes option pricing problem in mathematical finance: Generalization and extensions for a large class of stochastic processes", J.Phys.I France 4, 863-881 (1994)

q       D. Sornette, A. Johansen and J.-P. Bouchaud, "Stock market crashes, Precursors and Replicas", J.Phys.I France 6, n1, 167-175 (1996)

Black Hole Entropy

q       Strominger and C. Vafa, ``Microscopic Origin of the Bekenstein-Hawking Entropy", Phys. Lett. B379 (1996) 99-104

q       Juan M. Maldacena, ``Black Holes in String Theory", hep-th/9607235.

q       Juan Maldacena and Andrew Strominger, `` Statistical Entropy of Four-Dimensional Extremal Black Holes", Phys.Rev.Lett. 77 (1996) 428-429

Bose-Einstein Condensation in Atomic Gases - you should choose a particular topic yourself