Starting Tuesday, January 16th, 2018 in Room 356 A, Condorcet Bldg, Paris Diderot's Main Campus. A 30 hour lecture set (15 lectures). 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 2ch1: 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 3ch1: 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 5ch2: 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 6ch3: 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 7ch3: 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 9ch3 : 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 10ch4: 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 11ch4: 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 12ch5: Quantum Dynamics with a thermostat: System and bath. A bath made of oscillators. Quantum Langevin Equation. Lecture 13ch5: cont'd. Quantum Brownian Motion. ch6: Quantum Criticality, quenches and coarsening. Lecture 14ch6: cont'd. |