Physics of random and disordered systems
PHYS-645 / 3 crédits
Enseignant: Müller Markus
Langue: Anglais
Remark: Next time: Postponed to Fall 2024
Frequency
Every year
Summary
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
Content
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: Wignerâs 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
Keywords
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
Resources
Bibliography
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)