Physics of random and disordered systems
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)
- Type: optionnel