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 :
- 11 june 2014 : Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations in rings and hollow cylinders
- 10 june 2015 : Role of contacts in WL measurements and nonlocality of quantum transport
- 08 june 2016 : Anderson localisation of cold atoms in a disordered speckle potential
- 29 march 2017 : Quantum electronic transport in narrow 2D disordered metallic wires — solutions
- 30 march 2018 : Non-linear conductance of a coherent metallic wire — Effect of decoherence on CBS and Anderson localisation — solution pb 1 — solution pb 2
- 5 april 2019 : Metal insulator (Anderson) transition in 2D ? – solutions
- 3 april 2020 : DoS correction and AA correction – Self consistent theory of localization in finite media – correction of pb1 – correction of pb2
- 2 april 2021 : Magnetoconductance oscillations in a ring — CBS versus optical coherence ; correction
- 8 april 2022 : Weak localization correction in a hollow cylinder — Speckle correlations and memory effect ; correction pb1
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) :
- (pedagogical presentation based on path integral) : S. Chakravarty & A. Schmid, « Weak localization: the quasiclassical theory of electrons in a random potential« , Phys. Rep. 140, 193-236 (1986) ;
- (emphasize on scaling theory) B. Kramer & A. MacKinnon, « Localization: theory and experiment« , Rep. Prog. Phys. 56, 1469-1564 (1993) ;
- (emphasize on interaction effects) P. A. Lee & T. V. Ramakrishnan, « Disordered electronic systems« , Rev. Mod. Phys. 57, 287-337 (1985) ;
- Review articles (experiment oriented) :
- (emphasize on WL in 2D) G. Bergmann, « Weak localization in thin films« , Phys. Rep. 107, 1-58 (1984)
- (emphasize on fluctuations and AB oscillations) S. Washburn & R. Webb, « Aharonov-Bohm effect in normal metal. Quantum coherence and transport« , Adv. Phys. 35, 375-422 (1986)
- (emphasize on quantum oscillations) A. G. Aronov & Yu. V. Sharvin, « Magnetic flux effects in disordered conductors« , Rev. Mod. Phys. 59, 755 (1987)