M2 SC: Out of Equilibrium Statistical Mechanics, Classical and Quantum

Written Exam: Tuesday March 13th, 2018, 09:00-12:00, Room 307 [24-34], Jussieu Campus. All hand-written documents are allowed. No electronic devices allowed (not even the cell phone).

Starting Tuesday, January 16th, 2018. A 30 hour lecture set (15 lectures).

Tuesdays 08:45-10:45: On the Jussieu Campus, Université Pierre et Marie Curie. Room 203, Towers 14/24.

Thursdays 11:00-13:00: On the Paris Rive Gauche Campus, Université Paris Diderot. Room 302 A, Condorcet Bldg.

Some useful problems to work your way through the lectures (feel free to ask for help if you get stuck).

Some fully written out solutions by the 2017 graduates: Differential calculus likes Stratonovich discretization (by Bruno V.); A solvable master equation and dynamical complexity (by Martin M.); Glauber dynamics and the FDT (by Kevin B.); Kawasaki dynamics (by Sebastian G.); Triplet annihilation (by Bruno V.).

More solutions are expected from the 2018 class: Playing around with stochastic calculus (by Mallory D.); Recipe for a Gaussian white noise (by Aigars L.); Quantum formulation of classical stochastic dynamics (by Ludovico C.); Dean-Kawasaki Equation (very soon, by Pierre M.).

Lecture 1

ch1: Methods of stochastic dynamics: A review and some new things. Master Equation/Fokker-Planck and Langevin, and path integrals (Janssen-De Dominicis).

Lecture 2

ch1: cont'd. Equilibrium vs Nonequilibrium, Fluctuation-dissipation theorem, large deviations, Gallavotti-Cohen, Onsager and Green-Kubo relations.

Problems 1,2 3 cover chapter 1. A good thing is to go through Julien Tailleur's lectures. Textbooks on this topic are those by Risken, Van Kampen or Gardiner.

Lecture 3

ch1: cont'd. Gallavotti-Cohen, Onsager and Green-Kubo relations. Reversibility vs irreversibility (by the example).

Problem 4 is about the Glauber dynamics and the fluctuation-dissipation theorem. It's a good exercise to go through (covers the master equation, detailed balance, linear response). 

ch2: Critical Dynamics: Dynamics in the 1d Ising model and quantum spin chains. Persistence, coarsening.

Best textbook here is that by Uwe Täuber, which I warmly recommend. Else there is the 1977 review by Halperin and Hohenberg themselves. See also the exercise on the quantum representation of a master equation.

Lecture 4

ch2: cont'd. Halperin and Hohenberg classification.

See the exercise on Model B dynamics and the Kawasaki rules.

Lecture 5

ch2: cont'd. Dynamical universality.

ch3: Driven Systems: Diffusive systems and long-range interactions.

For Driven Diffusive Systems, one may have a look at a review or at the book by Beate Schmittmann and Royce Zia.

Lecture 6

ch3: cont'd. Strongly driven systems. Anomalous relaxation. Possibility of phase transitions in d=1.

A taste of the matrix ansatz method to find the steady-state distribution of an exclusion process. Other methods, specific to dimension 1, can be found in the review by Gunter Schütz.

Lecture 7

ch3: cont'd. The Matrix Ansatz in exclusion processes.

Lecture 8

Lecture 8 might actually replaced with a 3 hour tutorial (as in 2017). To be discussed and decided after a few lectures.

Lecture 9

ch3 : cont'd. Effect of a drive on a critical point.

ch4: Population Dynamics: Connections between a master equation and a many-body quantum problem.

It may be good to refresh your memory or learn about second quantization as seen in the quantum many-body problem. C. Mora's notes on the topic are very useful.

Lecture 10

ch4: cont'd. Doi-Peliti formalism. Reaction-Diffusion processes. Anomalous scaling. Two-species pair annihilation and segregation.

Check your understanding of this rather dense chapter with the Triplet annihilation exercise.

Lecture 11

ch4: cont'd. Directed Percolation and the contact Process. Epidemics. Nonequilibrium Phase Transitions and new universality classes. Networks as growth processes. Epidemics on networks.

Not in 2016-2017 nor in 2017-2018 : ch5: Grains: Statics and dynamics. Edwards measure. Granular gases. ch5: Glasses: Phenomenology. Mode-coupling Theory. Statics vs. Dynamics.

Lecture 12

ch5: Quantum Phase Transitions: Dynamics at zero temperature. Classical to Quantum correspondence. The physics of a quantum phase transition.

Lecture 13

ch5: cont'd.

ch6: Quantum Dynamics with a thermostat: System and bath. A bath made of oscillators. Quantum Langevin Equation.  Quantum Brownian Motion.

Lecture 14

ch6: cont'd.

Lecture 15

ch7: Nonequilibrium quantum dynamics: Keldysh formalism.

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