Physics of random and disordered systems

This course provides an overview of salient phenomena, concepts and theoretical approaches to a wide variety of random processes and disordered systems, with an emphasis on intuition and physical insight.

• Random walks, diffusion
• Directed polymers in random media,
• Roughening and pinning of interfaces

2) Localization of particles and waves:

• Weak and strong (Anderson) localization
• Many-body localization: concepts, ideas, phenomenology
• Strong randomness approach

3) Random matrix theory:

• Classification of random matrix models, matrix ensembles.
• Distribution of eigenvalues, semicircle law, resolvent method.
• Level spacing statistics: Wigner’s surmise, Poisson vs Wigner-Dyson,
• (Coulomb gas method)

4) Spin glasses:

• Concepts, phenomenology, order parameters; random energy model, trap model
• Theory: droplets, replicas
• Mean field theory:

replica symmetry and its breaking;
cavity approach / message passing

5) (depending on time) The role of disorder in critical phenomena:

• Imry-Ma argument
• Harris criterion