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


Starting Tuesday, January 16th, 2018 in Room 356 A, Condorcet Bldg, Paris Diderot's Main Campus. A 30 hour lecture set (15 lectures).

Tuesdays 4pm-6 pm: tba
Thursdays 10 am-12pm: tba

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.).

Lecture 1

ch1: Methods of stochastic dynamics: A review and some new things. Master Equation/Fokker-Planck and Langevin, and paths 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 was actually replaced with a 3 hour tutorial. Check with you fellow students for the solutions if you were unable to attend on thursday Feb 9th. Update: these will be posted momentarily.

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 : ch5: Grains: Statics and dynamics. Edwards measure. Granular gases. ch5: Glasses: Phenomenology. Mode-coupling Theory. Statics vs. Dynamics.

Lecture 12

ch5: Quantum Dynamics with a thermostat: System and bath. A bath made of oscillators. Quantum Langevin Equation.

Lecture 13

ch5: cont'd. Quantum Brownian Motion.

ch6: Quantum Criticality, quenches and coarsening.

Lecture 14

ch6: cont'd.




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