
MATH 1512 Instructor Jean Bellissard Professor of Mathematics and Physics School of Math, Skiles 132 , Physics Howey W511 Phone: (404) 3852179 (Math), (404) 3852509 (Phys) Fax: (404) 8944409 email: jeanbel@math.gatech.edu 
Lectures: Office Hours: Dates: 
Howey L2
TuesdayThursday 3:054:25PM by appointment August 22nd till December 7th, 20 

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, FokkerPlanck eq., 
The Boltzmann equation for dilute
systems: computation of transport coefficients 
Microscopic quantum models: complete
positivity, Markov approximation, Lindbladtype models, dilation
& noise 
1 Biology: molecular
motors, ratchets, cargo, motions in cells. 
2 Solid State physics: conduction
in periodic metal, aperiodic solids, GreenKubo formula 
3 Quantum Computing: measurement,
trapped ions, other systems, 
4 Deterministic Chaos Approach: fluctuation
of entropy production, CohenGallavotti theorem 
Textbooks  M. Le Bellac, F. Mortessaigne, G.
G. Batrouni, Equilibrium and
NonEquilibrium 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. 
Student Name 
Title 
Date 
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 NonEquilibrium Identities 
November 16, 2006 
Grigo, Alexander  The chaotic hypothesis and the
GallavottiCohen theorem 
November 21, 2006 
Jen, HsiangHua  Decoherence and quantum information 
November 28, 2006 
Joh, InHo  Fluctuation and irreversibility in
cosmology 
November 30, 2006 
Matsuoka, Yamato  Selforganized 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 
Phone: (404) 8945201 Fax: (404) 8949958 Address: 837 State Street, Atlanta, GA 303320430 