S  C  H  O  O  L     O F

P  H  Y  S  I  C  S

PHYS-7123 Statistical Mechanics II  (Fall 2006)

MATH 1512   Instructor
Jean Bellissard
Professor of Mathematics and Physics
School of Math, Skiles 132 ,
Physics Howey W511

Phone: (404) 385-2179 (Math),
              (404) 385-2509 (Phys)
Fax: (404) 894-4409
e-mail: jeanbel@math.gatech.edu


Office Hours:

Howey  L2  Tuesday-Thursday 3:05-4:25PM

by appointment

August 22nd till December  7th, 20

Students seminars begin on November 9th

See list below

This course intends to give the basic tools to deal with
Nonequilibrium Statistical Physics.
In the first part the phenomenological aspects will be presented. From the linear response theory
various macroscopic non linear equation equations will be derived (heat equation, diffusion equation,
fluid dynamics). More microscopic approaches will be investigated (Brownian motion, Drude
model for electrons, master equations for atom-radiation interaction). This will lead to the
Boltzmann equation (dilute classical systems) and to the Lindbladian description of quantum

In the second part of the course, depending upon students interest and time left, some applications
will be treated through student seminars. Among them applications to Biology (molecular motors), Quantum
Computing (measurement), Solid State Physics (quantum dissipation and Green-Kubo
formula in aperiodic solids), Chaos-like approach to
Nonequilibrium (universal fluctuations
of entropy production, the Cohen-Gallavotti theorem)
could be treated

Course Outline

Basic aspects

Equilibrium Statistical Physic: microstates, Gibbs states, conserved quantities, Lagrange multipliers
The local equilibrium approximation: densities, currents, conservation laws, entropy production
Linear Response Theory: Onsager coefficients, reciprocity relations, positivity, transport coefficients
Macroscopic equations: heat equation, diffusion equation, equations for fluid dynamic
Microscopic models (classical case): Brownian motion, Drude model, Master equation, Fokker-Planck eq.,
The Boltzmann equation for dilute systems: computation of transport coefficients
Microscopic quantum models: complete positivity, Markov approximation, Lindblad-type models,  dilation & noise

Some potential applications
(to be chosen by students)

1- Biology:  molecular motors, ratchets,  cargo, motions in cells.
2- Solid State physics: conduction in periodic metal, aperiodic solids,  Green-Kubo formula
3- Quantum Computing: measurement, trapped ions, other systems,
4- Deterministic Chaos Approach: fluctuation of entropy production, Cohen-Gallavotti theorem

Textbooks   M. Le Bellac, F. Mortessaigne, G. G. Batrouni, Equilibrium and Non-Equilibrium Statistical Mechanics, Cambridge University Press (2004)
J. Bellissard  Mécanique Statistique des Systèmes hors d'Equilibre. (pdf file in French)
Seminars (list)
Each regular student will be invited to prepare and deliver a lecture on a topics of his choice, related to the main topics of the curriculum, in agreement with the instructor. The lecture should last for 1:10 hour, and will be presented in class during the last month before the exam week.

This lecture will be evaluated the following ground: (i) quality of the written report, (ii) reference list (iii) quality of the oral presentation (iv) answer to questions.

Final Exam The evaluation grade given for the student seminars will serve as a final exam.

Seminars: list and dates  back to "Seminars", back to beginning

         Student Name
Balaraman, Gouthaman S. Ratchet models for molecular motors in biology
November 9, 2006
Bookjans, Eva M. Dissipative aspects of laser cooling
November 14, 2006
Bowlan, John M.
Jarinsky Non-Equilibrium Identities
November 16, 2006
Grigo, Alexander The chaotic hypothesis and the Gallavotti-Cohen theorem
November 21, 2006
Jen, Hsiang-Hua Decoherence and quantum information
November 28, 2006
Joh, In-Ho Fluctuation and irreversibility in cosmology
November 30, 2006
Matsuoka, Yamato Self-organized criticality: applications in dissipative systems
December 5, 2006
Singh, Abhinav Dissipation and entropy in Hopfield networks
December 7, 2006
Lippolis D
Scattering Theory of Transport
December 12, 2007

Thursday October 19th, 2006,
Earl McDaniel Memorial Colloquium (Physics)

Steve Chu, U C Berkeley
"The Energy Problem and what we can do about it"
Howey Lecture Room 4 at 3:00 pm
Reception at 2:15 in Howey N201

Final week: December 5 & 7th, 2006

(404) 894-5201 Fax: (404) 894-9958
Address: 837 State Street, Atlanta, GA 30332-0430