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Mathematics and Physics of Anderson Localization: 50 Years After
By Cambridge University
Mathematics and Physics of Anderson Localization: 50 Years After episodes
- Progress in rigorous multi-particle localization: Simpler proofs of stronger resultsTchoulaevski, V (Université de Reims Champagne-Ardenne)Friday 21 September 2012, 15:00-15:4042 min
- Spreading in potentials random in space and timeFishman, S (Technion - Israel Institute of Technology)Friday 21 September 2012, 14:20-15:0041 min
- The low lying spectrum of one-dimensional random modelsKlopp, F (Université Pierre & Marie Curie-Paris VI )Friday 21 September 2012, 11:50-12:3045 min
- 41 min
- Enhancement of Superconductivity by Anderson LocalizationGornyi, I (Forschungszentrum Karlsruhe)Friday 21 September 2012, 10:10-10:5045 min
- Statistical mechanics approach to the random matrix modelsShcherbina, M (Institute for Low Temperatures, Kharkov)Friday 21 September 2012, 09:30-10:1044 min
- Anderson localization, topology, and interactionOstrovsky, P (Max Planck Institut für Festkörperforschung)Thursday 20 September 2012, 11:50-12:3042 min
- Universality of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matricesShcherbina, T (Institute for Advanced Study, Princeton)Thursday 20 September 2012, 11:10-11:5043 min
- Universal statistics for directed polymers and the KPZ equation from the replica Bethe AnsatzLe Doussal, P (École Normale Supérieure)Thursday 20 September 2012, 10:10-10:5044 min
- New results on Rademacher Fourier and Taylor seriesSodin, M (Tel Aviv University)Thursday 20 September 2012, 09:30-10:1034 min
About Mathematics and Physics of Anderson Localization: 50 Years After
From the publisher's feed
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/
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