Falling out of equilibrium in classical systems: simple examples showing the role played by flat directions in the
energy landscape (the oscillator and the scalar field); coarsening: the phenomenon, dynamic scaling and the solution to the
O(N) model; nucleation and growth; relaxation in glasses; driven dynamics (rheology, two thermal baths).
Quantum glasses: relaxation, driven dynamics (two thermal baths).
Annealing and the Kibble-Zurek mechanism.
Classical stochastic Brownian dynamics: Langevin equation derived for an
isolated system's with an oscillators thermal bath; Martin-Siggia-Rose path integral.
Quantum mechanics: Green functions for Bosons and Fermions (definitions, conventions); linear response and Kubo formula; Feynman path integral (time-ordered); Schwinger-Keldysh path integrals (symmetric correlations).
Oscillators Feynman-Vernon model and the Caldeira-Leggett localisation; electronic environments; spin baths (short and quick reminder of all of this since it will be covered in more detail by other lecturers).
Matsubara imaginary time formalism; quenched disorder: replicas for equilibrium dynamics; mean-field models [rotors, p-spin and O(N) models]; second and first order phase transitions, the role of the bath.
Classical stochastic processes: in Fokker-Planck formalism with operators; in
Martin-Siggia-Rose with symmetries.
Quantum mechanical systems: KMS condition, canonical and gran-canonical fluctuation-dissipation theorems; Schwinger-Keldysh field theory; initial conditions and factorisation of the density matrix.
Mean-field models [rotors, p-spin and O(N) models]: how to deal with
SU(2) spins?; how to deal with the bath?
Tricks to solve the equations numerically and analytically.
Second and first order dynamic phase transitions.
The role of the bath.
Effective temperatures; quantum mechanical formalism?