Waves in disordered media and localization phenomena - Département de Physique de l'Ecole Normale supérieure

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Waves in disordered media and localization phenomena

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Faculty : Christophe Texier (LPTMS, Univ. Paris Sud)
Chargé de TDNicolas Cherroret (LKB, UPMC)
ECTS credits : 3
Language of instruction : Anglais
Site web : http://lptms.u-psud.fr/christophe_texier/enseignements/enseignements-en-master/onde-en-milieu-desordonne/

Description

We study the problem of transport and localization in disordered systems, when INTERFERENCE is present, as characteristic for waves. A wave propagates in some medium (be it vacuum), and interference occurs when different waves overlap, for example scattered from different positions with various wavevectors. We want to describe the propagation of the wave over long distances and for long times. Physical situations of this type cover the propagation of light in a turbid medium, electronic matter waves in conventional metals at low temperature, acoustic waves in a concert hall with complicated shape, seismic waves multiply scattered inside the earth, atomic matter waves in the presence of a disordered potential, etc. The emphasis is put on experimental situations met in solid state samples and (ultra-)cold atomic gases.

Content

1 Introduction : Disorder is everywhere

1.1 Disorder in condensed matter
1.2 Disorder in cold atomic gases
1.3 Importance of disorder : how would be the world without disorder ?
1.4 The physics of diffusion
1.5 How to model disorder ? What is measured ? What should be studied ?

2 Anderson localisation in one dimension

2.1 Models
2.2 Transfer matrix approach
2.3 Detailed study of a fully continuous model
2.4 Experiment with cold atoms
2.5 Transfer matrix and scattering matrix : Anderson localisation vs Ohm‚Äôs law
2.6 Self-averaging and non self-averaging quantities
2.7 Extension to quasi-1D case : qualitative description

3 Scaling theory : qualitative picture

3.1 What is a scaling theory ?
3.2 Dimensionless conductance
3.3 Scaling in 1D systems
3.4 Quasi-1D systems
3.5 Scaling in any dimension
3.6 d=2
3.7 d=3
3.8 d>3

4 Weak disorder : perturbative (diagrammatic) approach

4.1 Introduction
4.2 Averaging Green function
4.3 Kubo formula
4.4 Correlations between Green functions
4.5 Quantum correction to classical transport : weak localisation
4.6 Anomalous magnetoconductance
4.7 Kubo vs Landauer : short range vs long range
4.8 Coherent Back-scattering (light)
4.9 Conductance fluctuations (electrons)
4.10 Speckle pattern (light)
4.11 Conclusion : a probe for quantum coherence

5 Toward strong disorder ‚Äì Scaling theory : quantitative

5.1 Self-consistent theory of localization
5.2 Importance of symmetry properties
5.3 Transport by thermal hopping

6 Dephasing and decoherence

6.1 Coupling with the environment and the induced dephasing
6.2 Microscopic processes leading to decoherence
6.3 Bloch oscillations and the restoration of classical transport
6.4 Effect of decoherence on weak localization
6.5 Effect of decoherence on CBS
6.6 Diffusive wave spectroscopy

7 Interaction effects

7.1 Altshuler-Aronov correction to conductivity (a local thermometer)
7.2 Decoherence by electronic interactions
7.3 (More advanced topics)

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Next student seminar :
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Experimental Internship - Undergraduate program
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News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr