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Localization phenomena in disordered quantum systems
The aim of this lecture is to provide a description of quantum transport in disordered systems, with an emphasis on important phenomena like weak localization, Anderson localization and the Anderson metal-insulator transition. During the lecture, a number of important theoretical tools needed to describe quantum particle scattering in the presence of spatial disorder will be introduced in a pedagogical fashion, such as the Green's function technique, diagrammatic approaches to weak localization and transfer matrices. The lectures will be also illustrated by experimental examples and tutorials, especially taken from the physics of quantum gases and condensed matter.
Syllabus
1 Introduction and elements of scattering theory
1.1 Disorder in condensed matter, quantum gases and everyday life
1.2 Scattering theory: main concepts
1.3 Diffusion in disordered media and beyond
Tutorial
2 Weak disorder : perturbative (diagrammatic) approach
2.1 The Green's function technique in disorder
2.2 Correlations between Green functions
2.3 Multiple scattering as a diffusion process: microscopic derivation
2.4 Experiments
Tutorial
3 Weak localization in electronic transport
3.1 Kubo formula and Drude conductivity
3.2 Quantum corrections : weak localization
3.2 Anomalous magnetoconductance
Tutorial
4 Coherent backscattering effect
4.1 Introduction and qualitative description
4.2 Rigorous calculation, impact of decoherence
4.3. Experiments
Tutorial
5 Anderson localization in one dimension
5.1 Detailed study of a 1D Kronig-Penney disordered model
5.2 Transfer and scattering matrices
5.3 Anderson localization vs Ohm's law. Experiments
5.4 Conductance fluctuations and Fokker-Planck equation
6 Scaling theory of localization
6.1 Introduction
6.2 Thouless number and Thouless criterion
3.3 Scaling hypothesis and scaling function
3.4 Anderson quantum phase transition
7 Toward strong disorder, self-consistent theory of localization
5.1 Self-consistent theory of localization
5.2 Anderson critical point, critical exponents
5.3 Quantum transport of wave packets in disorder
5.4 Experiments
Tutorial
Evaluation
Written - 9am 12pm - Sorbonne Université
Prerequisites