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Mathematics and Physics of Anderson Localization: 50 Years After
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Mathematics and Physics of Anderson Localization: 50 Years After

Author: Cambridge University

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In his seminal paper Absence of diffusion in certain random lattices (1958) Philip W. Anderson discovered one of the most striking quantum interference phenomena: particle localization due to disorder. Cited in 1977 for the Nobel prize in physics, that paper was fundamental for many subsequent developments in condensed matter theory. In particular, in the last 25 years the phenomenon of localization proved to be crucial for the understanding of the Quantum Hall effect, mesoscopic fluctuations in small conductors as well as some aspects of quantum chaotic behaviour.

Random Schrödinger operators are an area of very active research in mathematical physics and mathematics. Here the main effort is to clarify the nature of the underlying spectrum. In particular, it has been proved that in dimension one all states are localized, and in any dimension the random Schrödinger operator has dense point spectrum for large enough disorder. Some open mathematical problems of major importance include the long-time evolutions of a quantum particle in a weakly disordered medium and existence of absolutely continuous spectrum in three dimensions. The expected transition from localized (point spectrum) to extended eigenstates (absolutely continuous spectrum) will also be addressed.

Read more at: http://www.newton.ac.uk/programmes/MPA/
130 Episodes
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Progress in rigorous multi-particle localization: Simpler proofs of stronger results

Progress in rigorous multi-particle localization: Simpler proofs of stronger results

2012-09-2541:59

Tchoulaevski, V (Université de Reims Champagne-Ardenne) Friday 21 September 2012, 15:00-15:40
Spreading in potentials random in space and time

Spreading in potentials random in space and time

2012-09-2540:07

Fishman, S (Technion - Israel Institute of Technology) Friday 21 September 2012, 14:20-15:00
The low lying spectrum of one-dimensional random models

The low lying spectrum of one-dimensional random models

2012-09-2544:13

Klopp, F (Université Pierre & Marie Curie-Paris VI ) Friday 21 September 2012, 11:50-12:30
Near integrable systems

Near integrable systems

2012-09-2540:53

Bogomolny, E (Université Paris-Sud 11) Friday 21 September 2012, 11:10-11:50
Enhancement of Superconductivity by Anderson Localization

Enhancement of Superconductivity by Anderson Localization

2012-09-2544:10

Gornyi, I (Forschungszentrum Karlsruhe) Friday 21 September 2012, 10:10-10:50
Statistical mechanics approach to the random matrix models

Statistical mechanics approach to the random matrix models

2012-09-2543:21

Shcherbina, M (Institute for Low Temperatures, Kharkov) Friday 21 September 2012, 09:30-10:10
Anderson localization, topology, and interaction

Anderson localization, topology, and interaction

2012-09-2441:41

Ostrovsky, P (Max Planck Institut für Festkörperforschung) Thursday 20 September 2012, 11:50-12:30
Universality of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices

Universality of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices

2012-09-2442:03

Shcherbina, T (Institute for Advanced Study, Princeton) Thursday 20 September 2012, 11:10-11:50
Universal statistics for directed polymers and the KPZ equation from the replica Bethe Ansatz

Universal statistics for directed polymers and the KPZ equation from the replica Bethe Ansatz

2012-09-2443:02

Le Doussal, P (École Normale Supérieure) Thursday 20 September 2012, 10:10-10:50
New results on Rademacher Fourier and Taylor series

New results on Rademacher Fourier and Taylor series

2012-09-2433:30

Sodin, M (Tel Aviv University) Thursday 20 September 2012, 09:30-10:10
Diffusion for a quantum particle coupled to a phonon gas

Diffusion for a quantum particle coupled to a phonon gas

2012-09-2443:49

De Roeck, W (Universität Heidelberg) Wednesday 19 September 2012, 16:10-16:50
Supersymmetry in localization/delocalization problems

Supersymmetry in localization/delocalization problems

2012-09-2442:54

Disertori, M (Université de Rouen) Wednesday 19 September 2012, 15:00-15:40
Localization for Linearly Reinforced Random Walks and Vertex Reinforced Jump Processes (iii)

Localization for Linearly Reinforced Random Walks and Vertex Reinforced Jump Processes (iii)

2012-09-2439:06

Crawford, N (Technion - Israel Institute of Technology) Wednesday 19 September 2012, 14:20-15:00
Kolmogorov turbulence, Anderson localization and KAM integrability

Kolmogorov turbulence, Anderson localization and KAM integrability

2012-09-2445:04

Shepelyansky, D (Université Paul Sabatier Toulouse III) Wednesday 19 September 2012, 11:50-12:30
Anomalously localized states in the one-dimensional Anderson localization model at E=0

Anomalously localized states in the one-dimensional Anderson localization model at E=0

2012-09-2443:53

Kravtsov, V (Abdus Salam International Centre for Theoretical Physics) Wednesday 19 September 2012, 10:10-10:50
Edge reinforced random walks, Vertex reinforced jump process and the SuSy hyperbolic sigma model (II)

Edge reinforced random walks, Vertex reinforced jump process and the SuSy hyperbolic sigma model (II)

2012-09-2141:25

Tarres, P (University of Oxford) Wednesday 19 September 2012, 09:30-10:10
Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function

Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function

2012-09-2139:08

Keating, J (University of Bristol) Tuesday 18 September 2012, 11:50-12:30
Classification and symmetry properties of scaling dimensions at Anderson transitions

Classification and symmetry properties of scaling dimensions at Anderson transitions

2012-09-2144:40

Mirlin, A (Universität Karlsruhe (TH)) Tuesday 18 September 2012, 11:10-11:50
Recent progress in the spectral theory of first order elliptic systems

Recent progress in the spectral theory of first order elliptic systems

2012-09-2140:59

Vassiliev, D (University College London) Tuesday 18 September 2012, 10:10-10:50
Topological phases of matter, Anderson localization/delocalization and anomalous transport law

Topological phases of matter, Anderson localization/delocalization and anomalous transport law

2012-09-2141:30

Ryu, S (University of Illinois at Urbana-Champaign) Tuesday 18 September 2012, 09:30-10:10
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