Mathematics and physics of Anderson localisation: 50 years after
MPA
14 July 2008 to 19 December 2008
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Programme theme
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.
The goal of the program is to bring together the world leaders in spectral theory of random Schrödinger operators and theoretical physicists successfully working on the problem of Anderson localization. Among the topics that will be addressed during the program are: The nature of critical phenomena associated with localization-delocalization transitions; The existence and statistical properties of extended states for D > 2 and the behaviour in the critical dimension D = 2; rigorous version of supersymmetric methods and of the nonlinear σ-model techniques; the localization-delocalization phenomena associated with the Integer Quantum Hall effect; rigorous mathematical understanding of the relation between magnetic Schrödinger operators and network models, and the connection with quantum percolation; localization in the presence of a random magnetic field; behaviour of products of random matrices and associated Lyapunov exponents; localization and delocalization in disordered systems characterised by non-selfadjoint operators; dynamical localization in Quantum Chaotic systems; localization in systems with aperiodic potential, as well as in models with correlated or long-ranged disorder; localization in systems with nonlinearities, and localization-delocalization phenomena in disordered systems of interacting quantum particles.
Click here to download the programme's final scientific report
Preprints
| Title | Year | Programme |
|---|---|---|
On asymptotic behavior of multilinear eigenvalue statistics of random matricesAuthors: A Lytova, L Pastur |
2008 | MPA |
FORCE schemes on unstructured meshes II: nonconservative hyperbolic systemsAuthors: A Hidalgo, M Castro, C Pares, EF Toro, M Dumbser |
2008 | MPA |
Eigenvector localization for random band matrices with power law band widthAuthors: J Schenker |
2008 | MPA |
Diffusion of wave packets in a Markov random potentialAuthors: J Schenker, Y Kang |
2008 | MPA |
Workshops
Anderson localisation transition: introductory training course
14 July 2008 to 25 July 2008
Anderson localisation and related phenomena
18 August 2008 to 22 August 2008
Delocalization transition and multifractality
2 November 2008 to 6 November 2008
Classical and quantum dynamics in the presence of disorder
15 December 2008 to 19 December 2008
Mathematics and physics of disordered systems
17 September 2012 to 21 September 2012
Seminars
| Tuesday 29th July 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Andreas Ludwig University of California, Santa Barbara |
Room 1 | |
| Thursday 31st July 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Stanislav Molchanov University of North Carolina |
Room 1 | 
|
| Tuesday 5th August 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Jens Marklof University of Bristol |
Room 1 |
|
| Thursday 7th August 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Stanislav Molchanov University of North Carolina |
Room 1 |
|
| Tuesday 12th August 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Alexander Mirlin |
Room 2 | |
| Wednesday 13th August 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 | Room 2 | ||
| 16:00 to 17:00 |
Konstantin Khanin University of Toronto |
Room 2 | |
| Thursday 14th August 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Laszlo Erdos Ludwig-Maximilians-Universität München |
Room 2 | |
| Tuesday 26th August 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Franz Joachim Wegner Ruprecht-Karls-Universität Heidelberg |
Room 1 | |
| Wednesday 27th August 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 | Room 1 |
|
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| Thursday 28th August 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 | Room 1 | ||
| Tuesday 2nd September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Boris Shapiro Technion - Israel Institute of Technology |
Room 1 |
|
| Thursday 4th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 | Room 1 |
|
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| Tuesday 9th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Mikhail Titov Heriot-Watt University |
Room 2 | |
| Wednesday 10th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Vladas Sidoravicius IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro |
Room 2 | |
| Thursday 11th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Spectra of sparse random matrices and localisation on random graphs |
Room 2 | |
| Tuesday 16th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Igor Lerner University of Birmingham |
Room 1 |
|
| Wednesday 17th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Vladimir Falko Lancaster University |
Room 1 | |
| Thursday 18th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Antti Kupiainen University of Helsinki |
Room 1 |
|
| Friday 19th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Construction of KdV flow on generalised reflectionless potentials |
Room 1 |
|
| Tuesday 23rd September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Svetlana Jitomirskaya University of California, Irvine |
Room 1 | |
| Thursday 25th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Dmitry Savin Brunel University |
Room 1 | |
| Tuesday 30th September 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Victor Tchoulaevski Université de Reims Champagne-Ardenne |
Room 2 | |
| Thursday 2nd October 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Wojciech De Roeck Ruprecht-Karls-Universität Heidelberg |
Room 2 | |
| Tuesday 7th October 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Benjamin Schlein Rheinische Friedrich-Wilhelms-Universität Bonn |
Room 1 |
|
| Wednesday 8th October 2008 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Gregory Falkovich University of California, Irvine and Weizmann Institute of Science |
Room 1 | |
| Thursday 9th October 2008 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Sergey Nazarenko University of Warwick |
Room 1 |
|
| 14:00 to 15:00 |
Patricio Leboeuf Université Paris Saclay |
Room 1 |
|
| Tuesday 14th October 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Dmitrii Shepelyansky Université Paul Sabatier Toulouse III |
Room 1 |
|
| Wednesday 15th October 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Christopher Mudry |
Room 1 | |
| Tuesday 21st October 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Vladimir Akulin CNRS (Centre national de la recherche scientifique) |
Room 1 |
|
| Wednesday 22nd October 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Vaclav Janis Academy of Sciences of the Czech Republic |
Room 1 |
|
| Thursday 23rd October 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 | Room 1 | ||
| Monday 27th October 2008 | |||
|---|---|---|---|
| 17:00 to 18:00 | Room 1 |
|
|
| Tuesday 28th October 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Mihai Stoiciu Williams College |
Room 1 |
|
| Thursday 30th October 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Michael Aizenman Princeton University |
Room 1 | |
| Tuesday 11th November 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
One-dimensional Anderson Model: Devil's Staircase of Statistical Anomalies |
Room 1 | |
| Thursday 13th November 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 | Room 1 | ||
| Thursday 20th November 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Yan Fyodorov Queen Mary University of London |
Room 1 | |
| Tuesday 25th November 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Jean-Marc Luck CEA/Saclay |
Room 1 |
|
| Tuesday 2nd December 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Hakan Tureci ETH Zürich |
Room 1 |
|
| Thursday 4th December 2008 | |||
|---|---|---|---|
| 14:00 to 15:00 | Room 1 |
|
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| Wednesday 10th December 2008 | |||
|---|---|---|---|
| 11:30 to 12:10 |
Peter Stollmann Technische Universität Chemnitz |
Room 2 | |
| 14:00 to 15:00 |
Mikhail Skvortsov Pereslavl-Zalessky of the Russian Academy of Sciences |
Room 2 | |
| 15:30 to 16:30 | Room 2 | ||
| Thursday 11th December 2008 | |||
|---|---|---|---|
| 14:00 to 14:40 |
Pragya Shukla Indian Institute of Technology |
Room 2 | |
| 14:40 to 15:20 |
Vincent Sacksteder Asia Pacific Center for Theoretical Physics |
Room 2 | |
Organisers
- Yan Fyodorov Brunel University
- Ilya Goldsheid
- Tom Spencer Institute for Advanced Study, Princeton
- Martin Zirnbauer Universität zu Köln
Speakers
- Michael Aizenman Princeton University
- Vladimir Akulin CNRS (Centre national de la recherche scientifique)
- Wojciech De Roeck Ruprecht-Karls-Universität Heidelberg
- Laszlo Erdos Ludwig-Maximilians-Universität München
- Vladimir Falko Lancaster University
- Gregory Falkovich University of California, Irvine and Weizmann Institute of Science
- Yan Fyodorov Brunel University
- Vaclav Janis Academy of Sciences of the Czech Republic
- Svetlana Jitomirskaya University of California, Irvine
- Konstantin Khanin Isaac Newton Institute
- Herve Kunz
- Antti Kupiainen University of Helsinki
- Patricio Leboeuf Université Paris Saclay
- Igor Lerner University of Birmingham
- Jean-Marc Luck CEA/Saclay
- Andreas Ludwig University of California, Santa Barbara
- Jens Marklof University of Bristol
- Alexander Mirlin
- Stanislav Molchanov University of North Carolina
- Christopher Mudry
- Sergey Nazarenko University of Warwick
- Vincent Sacksteder Asia Pacific Center for Theoretical Physics
- Dmitry Savin Brunel University
- Benjamin Schlein Rheinische Friedrich-Wilhelms-Universität Bonn
- Boris Shapiro Technion - Israel Institute of Technology
- Dmitrii Shepelyansky Université Paul Sabatier Toulouse III
- Pragya Shukla Indian Institute of Technology
- Vladas Sidoravicius IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro
- Mikhail Skvortsov Pereslavl-Zalessky of the Russian Academy of Sciences
- Mihai Stoiciu Williams College
- Peter Stollmann Technische Universität Chemnitz
- Victor Tchoulaevski Université de Reims Champagne-Ardenne
- Mikhail Titov Heriot-Watt University
- Hakan Tureci ETH Zürich
- Franz Joachim Wegner Ruprecht-Karls-Universität Heidelberg
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