M2 iCFP – Ondes en milieux désordonnés et phénomènes de localisation

Waves in disordered media and localisation phenomena


Master iCFP, Quantum physics

2013-2021 : Course & Exercices

Lectures given in collaboration with Nicolas Cherroret from  Laboratoire Kastler-Brossel, UPMC, Jussieu (and, from 2013 to 2016 with Dominique Delande)

Lecture notes (updated: 04/02/2021)


Program (10 lectures) :

1. Introduction : disorder is everywhere (NC)

TD : Bloch oscillations (DD)

TD : Wave diffusion through a slice of disordered medium (NC)

2. Anderson localisation in one dimension (CT)

TD : Thouless relation (CT)

TD : Localisation and Lishits tail in the Frisch-Lloyd model (CT)

TD : The Landauer approach and the distribution of the conductance (CT)

3. Scaling theory (NC)

TD : The scaling approach of 1D localisation — distribution of the transmission probability (CT)

TD : Ioffe-Regel criterion: matter waves versus electromagnetic waves (NC)

 4 to 6. Quantum transport in weakly disordered metals (CT)

TD : Classical and anomalous magneto-conductance (CT)

TD : Magneto-conductance of 2D metals (CT)

TD : Spin-orbit scattering and weak anti-localisation in metallic films (CT)

7. Universal conductance fluctuations (CT)

TD : Conductance fluctuations and correlations in narrow wires (CT)

8. Coherent back-scattering (NC)

TD : Shape of the coherent back-scattering peak (DD)

9. Self-consistent theory of localisation (NC)

TD : Kicked rotor (DD)

10. Dephasing and decoherence (NC)

 (Interaction effects, CT)

TD : Decoherence by electronic interactions — Influence functional approach (CT)


Exams  :

Bibliography :

  • A book (emphasize on 1D case and exact results) : J.-M. Luck, « Systèmes désordonnés unidimensionnels« , CEA, collection Aléa Saclay (1992).
  • A book (advanced, with emphasize on strong localisation) : I. M. Lifshitz, S. A. Gredeskul & L. A. Pastur, « Introduction to the theory of disordered systems« , John Wiley & Sons (1988).
  • A book (introductory, emphasize on mesoscopic physics, brief introduction to diagrammatic approach) : S. Datta, « Electronic transport in mesoscopic systems« , Cambridge University Press (1995)
  • A complete and pedagogical presentation (photons and electrons in parallel, emphasize on weak localisation regime) : E. Akkermans & G. Montambaux, « Mesoscopic physics of electrons and photons« , Cambridge University Press (2007) ; in french : EDP Sciences, CNRS éditions (2004)
  • Introductory articles (weak localisation regime) : B. L. Altshuler & P. A. Lee, « Disordered electronic systems« , Physics Today 41, 36-44 (1988) ; R. A. Webb & S. Washburn, « Quantum interference fluctuations in disordered metals« , Physics Today 41, 46-53 (1988) ; and, (atomic physics) : L. Sanchez-Palencia and M. Lewenstein, « Disordered quantum gases under control« , Nature Phys. 6, 87-95 (Feb. 2010).
  • Review articles (theory oriented) :
  • Review articles (experiment oriented) :

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