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The list of references below (in
arbitrary order) is only to guide those who are interested and is by no means exhaustive.
For many of the linked papers you, or your instituttion, must have a subscription to be able to
download the pdf file.
1. The Source
2. Reviews
3. Reports on observations of Anderson Localization
4. General theory
5. Interactions
6. Quasi one-dimensional
7. Anderson Model
8. Quantum Hall effect
9. Mathematical proof of Anderson Localizations
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1. The Source
Philip
Anderson
Absence of Diffusion in Certain Random Lattices
Phys. Rev. 109, 1492 - 1505 (1958).
The following, absolutely brilliant, paper is not directly connected to localization,
but should be read by any scientist. It is widely seen as the best description of the limitations
of absolute reductionism.
Philip Anderson
More is different
Science 177, 393-396 (1972).
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In case you cannot access the above link we post here directly the
pdf file (with explicit permission from the author).
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2. Reviews
Nevill Mott
Metal insulator transition
Rev. Mod. Phys. 40, 677 - 683 (1968).
Sajeev
John
Localization of light
Physics Today, May 1991.
B.A. van Tiggelen
Anderson Localization of waves - course at Les Houches 1998
D.
J. Thouless
Electrons in disordered systems and the theory of localization
Phys. Rep., 13C, 93 (1974).
D.
Vollhardt and P. Wölfle
Self-consistent theory of Anderson Localization,
in: Electronic Phase Transitions,
eds. W. Hanke and Ya. V. Kopaev (North-Holland, Amsterdam, 1992),
Chapter 1, p. 1.
Leonid
Pastur and Alexander Figotin
Spectra of Random and Almost-Periodic
Operators
(Springer-Verlag, 1992).
E.
Abrahams, P.W. Anderson, D.C. Licciardello, and T.V. Ramakrishnan
Scaling theory of localization: absence of quantum diffusion in two
dimensions
Phys. Rev. Lett. 42, 673 - 676 (1979).
P.A. Lee and T.V. Ramakrishnan
Disordered electronic systems
Rev. Mod. Phys. 57, 287 (1985).
=================================
3. Reports on observations of Anderson Localization
Martin Störzer, Peter Gross, Christof M. Aegerter, and Georg
Maret
Observation of the critical regime near Anderson Localization of light
Phys. Rev. Lett. 96, 063904 (2006).
Diederik S. Wiersma, Paolo Bartolini, Ad Lagendijk, and Roberto Righini
Localization of light in a disordered medium
Nature 390, 671-673 (1997).
A.A. Chabanov, M. Stoytchev, and A. Z. Genack
Statistical signatures of photon localization
Nature 404, 850-853 (2000).
A. A. Chabanov and A. Z. Genack
Photon Localization in Resonant Media
Phys. Rev. Lett. 87, 153901 (2001).
Tal Schwartz, Guy Bartal1, Shmuel Fishman, and Mordechai Segev
Transport and Anderson Localization in disordered two-dimensional
Photonic Lattices.
Nature 446, 52-55 (2007).
J. Topolancik, B. Ilic, and F. Vollmer
Experimental Observation of Strong Photon Localization in
Disordered Photonic Crystal Waveguides
Phys. Rev. Lett 99, 253901 (2007).
Giacomo Roati, Chiara D'Errico, Leonardo Fallani, Marco Fattori, Chiara Fort,
Matteo Zaccanti, Giovanni Modugno, Michele Modugno1, and Massimo Inguscio
Anderson localization of a non-interacting Bose–Einstein
condensate
Letter to Nature 453, 895-898 (2008).
Juliette Billy, Vincent Josse, Zhanchun Zuo, Alain Bernard, Ben Hambrecht,
Pierre Lugan, David Clément, Laurent Sanchez-Palencia,
Philippe Bouyer, and Alain Aspect
Direct observation of Anderson localization of matter waves in a
controlled disorder
Nature 453, 891-894 (2008).
Julien Chabe, Gabriel Lemarie, Benoit Gremaud, Dominique Delande,
Pascal Szriftgiser, and Jean Claude Garreau
Experimental observation of the Anderson transition with atomic matter
waves.
H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov, and B.A. van Tiggelen
Localization of ultrasound in a three-dimensional elastic network.
R. Dalichaouch, J.P. Armstrong, S. Schultz, P.M. Platzmann, and S.L. McCall
Microwave localization by 2D random scattering
Nature 354, 53 (1991).
R. L. Weaver
Anderson localization of ultrasound
Wave Motion Volume 12, 129-142 (1990).
L. Ye, G. Cody, M. Zhou, and P. Sheng
Observation of bending wave localization and quasi mobility edge in two dimensions
Phys. Rev. Lett. 69, 3080 (1992).
=================================
4. General theory
P.A. Lee and T.V. Ramakrishnan
Disordered electronic systems
Rev. Mod. Phys. 57, 287 (1985).
B. Kramer and G. Schön, editors
Special issue on Anderson transition and mesoscopic fluctuations
Physica A 167, 1 (1990).
S. Fishman, D.R. Grempel, and R.E. Prange
Chaos, quantum recurrences and Anderson Localization
Phys. Rev. Lett. 49, 509 (1982).
M. Kaveh and N.F. Mott
The metal-insulator transition in 3D systems: a new view
J. Phys. C: Solid State Phys. 15 L697-L705 (1982).
D. Vollhardt and P. Wölfle
Anderson Localization in d<2 dimensions: a self-consistent diagrammatic theory
Phys. Rev. Lett. 45, 842 (1980).
S. John
Strong localization of photons in certain disordered dielectric superlattices
Phys. Rev. Lett. 58, 2486 - 2489 (1987).
P.W. Anderson
The question of classical localization: a theory of white paint?
Philos Mag. B 52, pp. 505–509 (1985).
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In case you cannot access the above link we post here directly the
pdf file (with explicit permission from the author).
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H.A. de Raedt, A. Lagendijk, and P. de Vries
Transverse localization of light
Phys. Rev. Lett. 62, 47 - 50 (1989).
B.A. van Tiggelen, A. Lagendijk and D.S. Wiersma
Reflection and transmission of waves near the localization threshold
Phys. Rev. Lett. 84, 4333 (2000).
S. E. Skipetrov and B. A. van Tiggelen
Dynamics of Anderson Localization in open 3D media
Physical Review Letters 96 043902 (2006)
F. Evers and A.D. Mirlin
Anderson Transitions
To appear in Rev. Mod Phys.
=================================
5. Interactions
L. Fleishman and P.W. Anderson
Interactions and the Anderson transition
Pjys. Rev. B 21, 2366 (1980).
B.L. Altshuler, A.G. Aronov, and D.E Khmelnitskii
Effects of electron-electron collisions with small energy transfers on quantum localisation
J. Phys. C 15, 7367 (1982).
D. M. Basko, I. L. Aleiner, and B. L. Altshuler
Metal-insulator transition in a weakly interacting many-electron
system with localized single-particle states
Ann. Phys. (N.Y.) 321, 1126 (2006).
A.S. Pokovsky and D.L. Shepelyanski
Destruction of Anderson loclizationL by a weak Nonlinearity
Phys. Rev. Lett. 100, 094101 (2008).
Rudolf A. Römer and Michael Schreiber
No Enhancement of the localization length for two
interacting particles in a random potential
Phys. Rev. Lett. 78, 515 (1997).
D. L. Shepelyansky
Coherent propagation of two interacting particles in a random potential,
Phys. Rev. Lett. 73, 2607 (1994).
=================================
6. Quasi one-dmensional
D. J. Thouless
Maximum metallic resistance in thin wires
Phys. Rev. Lett. 39, 1167 (1977).
P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher
New method for a scaling theory of localization
Phys. Rev. B 22, 3519 - 3526 (1980).
O.N. Dorokhov
Electron localization in a multichannel conductor
JETP 58, 606 (1983).
P.A. Mello, P. Pereyara and N. Kumar
Macroscopic approach to multichannel disordered conductors
Ann. Phys. 181, 290 (1988).
C.W.J. Beenakker
Random matrix theory of quantum transport
Rev. Mod. Phys. 69, 731 (1997).
=================================
7. Anderson Model
R. Abou-Chacra, P.W. Anderon, and D.J. Thouless
A self-consistent theory of localization
J. Phys. C: Solid State Phys. 6 1734-1752 (1973).
B. Bulka, M. Schreiber, and B. Kramer
Localization, quantum interference
and the metal-insulator transition
Z. Phys. B66 21 (1987).
A. MacKinnon and B. Kramer
One-parameter scaling of localization length and
conductance in disordered systems
Phys. Rev. Lett. 47, 1546 - 1549 (1981).
=================================
8. Quantum Hall effect
B. I. Halperin
Quantized Hall conductance, current-carrying edge
states, and the existence of extended states in a
two-dimensional disordered potential
Phys. Rev. B 25, 2185 - 2190 (1982).
H. P. Wei, D. C. Tsui and A. M. M. Pruisken
Localization and scaling in the quantum Hall regime
Phys. Rev. B 33, 1488 - 1491 (1986).
=================================
9. Mathematical proof of Anderson Localizations
Frohlich,
J., Spencer, T.:
Absence of diffusion in the Anderson tight-binding model for large
disorder or low energy.
Commun. Math. Phys. 88, 151 (1983).)
François
Delyon, Yves Lévy, and Bernard Souillard,
Anderson localization for multidimensional systems at large disorder or
large energy
Comm. Math. Phys. 100, 463-470 (1985).
M. Aizenman,
Localization at weak disorder: some elementary bounds,
Rev Math. Phys. 6 (5a), 1163-1182 (1994).
H. von Dreifus and A Klein
A new proof of localization in the Anderson tight binding model
Comm. Math. Phys. 124, 285-299 (1989).
M. Aizenman and S.A.Molchanov:
Localization at large disorder and at extreme energies:
an elementary derivation.
Comm. Math. Phys. 157, 245 (1993).
I. Ya. Gol'dshtein, S. A. Molchanov, and L. A. Pastur
A pure point spectrum of the stochastic one-dimensional Schrödinger operator
Functional Anal. Appl. 11, 1-8 (1977).
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