PHYS-645 / 3 crédits

Enseignant: Müller Markus

Langue: Anglais

Remark: Next time: Postponed to Fall 2024


Every year


Introduction to the physics of random processes and disordered systems, providing an overview over phenomena, concepts and theoretical approaches Topics include: Random walks; Roughening/pinning; Localization; Random matrix theory; Spin glasses; Disorder and critical phenomena


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.


1) Random processes:

  • 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


disordered systems, random processes, random matrix theory, localization, spin glasses

Learning Prerequisites

Required courses

Statistical physics I and II

Recommended courses

Quantum mechanics

Learning Outcomes

By the end of the course, the student must be able to:

  • Have an overview over and physical understanding of the phenomena in disordered systems
  • Know and explain the concepts, basic techniques and approaches to the main topics



There will be a Moodle link for this course

Moodle Link

Dans les plans d'études

  • Forme de l'examen: Oral (session libre)
  • Matière examinée: Physics of random and disordered systems
  • Cours: 42 Heure(s)
  • Type: optionnel

Semaine de référence

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