Beg Rohu, May 30-June 12, 2021
Methods for Non-Equilibrium Statistical Mechanics (12h)
1. Master Equation and stochastic processes:
The physics behind a master equation
Fokker-Planck equation
Stochastic calculus
A breather with a few useful examples
One final tool in the toolbox: path integrals
2. In, or out of, equilibrium
Characterizing equilibrium
A brief overview of fluctuation theorems
How about a single active particle
An active particle in a potential
Actually measuring the distance to equilibrium
3. Rare events
Kramers as usual
How about an active Kramers formula
For a particle subjected to a white but non-Gaussian noise
A trapping problem
4. Collective phenomena in active systems
Introduction, and the two-particle problem
From 2 to N particles
A detour via equilibrium
Mesoscopic description of scalar active matter
5. A chemical reaction
Mean-field and the importance of fluctuations
Langevin description, and beyond
Towards a quantum formulation
Exploiting the Doi-Peliti formalism
Back to the chemical reaction
The particular one-dimensional case
6. Epidemics
The SIR model and its connection to percolation
The SIS model, sandpiles, and the depinning transition
The SIS model and directed percolation
Connection to directed percolation
Dynamical scaling
Critical discussion of diffusive models. Epidemics on networks
Front propagation into an unstable state
Branching and annihilating random walks
7. Preys and Predators
Around Lotka and Volterra
Incorporating fluctuations, the two-species problem
Three-species population
A set of extended lecture notes