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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 |
Lectures: Office Hours: Dates: |
Howey L2
Tuesday-Thursday 3:05-4:25PM by appointment August 22nd till December 7th, 20 |
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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 |
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. |
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 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 |
Phone: (404) 894-5201 Fax: (404) 894-9958 Address: 837 State Street, Atlanta, GA 30332-0430 |