Course 1: Bulbul Chakrabarty
Lecture 1 - Overview
Lecture 2 - The Statistical Physics of Athermal Materials
- Lecture 2
Lecture 3 - Isostatic argument for frictional particles
Lecture 4 - Elasticity from gueage theory
Course 2: Leticia Cugliandolo
Lecture 1 - Out of equilibrium dynamics of complex systems
Lecture 2 - Coarsening
Lecture 3 - References and answers to questions
Lecture 4 - Disorder
Course 3: Manas Kulkarni
Course structure and reading material
Course 4: Gregory Schehr
Course outline
I) (Lecture 1 and 2) Introduction to Random Matrix Theory (RMT)
Lecture 1
Lecture 2
1) General overview of applications of RMT: from Wigner to Kardar-Parisi-Zhang (KPZ) equation
2) Ensembles of RMT
2.1) Wigner matrices
2.2) Rotationally inv. ens. of RMT
2.3) Joint law of eingenvalues for Gaussian Orthogonal and Unitary Ensembles (GOE/GUE)
3) Coulomb gas approach
3.1) Physical interpretation of the joint PDF of the eigenvalues and the log-gas
3.2) Discuss the Wigner semi-circle and its universality
4) Local statistics
4.1) Bulk (Wigner surmise)
4.2) Edge (Tracy-Widom fluctuations and applications to KPZ)
II) (Lecture 3-Lecture 4): Fermions and connections to RMT -- 1 lecture + 1/3 lecture
Lecture 3
Lecture 4
1) Harmonic potential without interactions at T=0 and the GUE
2) Finite Temperature and connections to KPZ
3) Interacting fermions and matrix models
III) (Lecture 4-5) Non-intersecting paths and Dyson’s Brownian motion
Lecture 5
1) Non intersecting Brownian motions and non-interacting fermions
2) Connection to RMT
3) Dyson’s Brownian motion
4) More recent developments
Course 5: Arnab Sen
Introduction to some basic notions of thermalization under unitary dynamics in many-body quantum systems, eigenstate thermalization hypothesis and its violations
- Integrable models (S=1/2 transverse field Ising model in one dimension, calculation of entanglement entropy, demonstration of volume law entanglement for high-energy states, locality of conservation laws)
- Quantum many-body scars in translationally invariant systems (PXP model etc, anomalous dynamics from special initial conditions, connection to lattice gauge theory)
- Many-body localization and the l-bit picture (emergent integrability, non-ergodic phase of matter)
- Periodically driven (Floquet) time crystals in many-body localized systems and breaking of discrete time-translation symmetry. Prethermal versions of time crystals without disorder
Background: Earlier lectures by Arul and Subroto in the Bangalore Stat. Phys. Schools.
Course 6: Hugo Touchette