Delocalization transition and multifractality

Workshop theme

As is well-known, by changing disorder potential in a single-particle quantum Hamiltonians one may induce a transition from localised to extended eigenstates (the Anderson delocalisation transition). Precisely at the point of the transition one expects a very non-trivial intensity pattern reflecting intriguing "multi-fractal" properties of the critical eigenstates (see the figure). This picture extends to a broader class of quantum systems, including, most prominently, those exhibiting Quantum Hall type transitions. It also has interesting counterparts beyond quantum mechanics in other disorder-induced critical phenomena.

In recent years considerable efforts were invested in performing large-scale numerical simulations of systems of that kind. This allowed both to test highly non-trivial analytical predictions for various critical statistics, and provided additional insights and the background for further theoretical understanding. The proposed 4-day workshop will bring together the researchers successfully working on the problem of Anderson de-localization transition, with emphasis on multifractality and its implications. We plan to review the state of the art in both numerical and analytical communities, to discuss conceptual as well as technical difficulties and to map new directions of research in this fascinating area of Theoretical Physics.

Multifractal wave function at the critical point (courtesy of F Evers, A Mildenberger and A Mirlin)

The Organisers would like to thank the following sponsors for their generous support of the event:

Timetable

Sunday 2nd November 2008
12:30 to 13:30	Lunch	No Room Required
15:20 to 16:10	Alexander Mirlin Anderson transitions: recent developments	No Room Required
16:10 to 16:40	Tea and Posters	No Room Required
16:40 to 17:30	Illya Gruzberg University of Chicago Critical wave functions, conformal invariance, and theories for quantum Hall transitions	No Room Required
17:30 to 19:00	Discussions	No Room Required
19:00 to 20:00	Dinner	No Room Required

Monday 3rd November 2008
09:00 to 09:50	Mikhail Feigelman L.D.Landau Institute for Theoretical Physics, Moscow Fractal superconductivity near localization threshold	No Room Required
09:50 to 10:40	Vladimir Kravtsov Abdus Salam International Centre for Theoretical Physics Multifractality of single-particle wave functions and superconductivity near the Anderson transition	No Room Required
10:40 to 11:10	Coffee and Posters	No Room Required
11:10 to 12:00	Akira Furusaki RIKEN Boundary multifractality and conformal invariance at 2D metal-insulator transition	No Room Required
12:00 to 12:50	Ferdinand Evers Multifractality in model systems for quantum Hall critical points	No Room Required
12:50 to 14:30	Lunch and Discussion	No Room Required
14:30 to 15:20	Christopher Mudry Quantum transport of 2D Dirac fermions: The case for a topological metal	No Room Required
15:20 to 16:10	Hideaki Obuse Kyoto University Multifractality at the metal-quantum spin Hall insulator transition in two dimensions	No Room Required
16:10 to 16:40	Tea and Posters	No Room Required
16:40 to 17:30	Minimal supporting subtrees for the free energy of polymers on disordered trees	No Room Required
17:30 to 19:00	Discussions	No Room Required
19:00 to 20:00	Dinner	No Room Required

Tuesday 4th November 2008
09:00 to 09:50	John Chalker University of Oxford Class C network models, and quantum and classical delocalisation transitions.	No Room Required
09:50 to 10:40	Victor Kagalovsky Sami Shamoon College of Engineering, Beer-Sheva, Israel Chalker-Coddington network model and its applications to various quantum Hall systems	No Room Required
10:40 to 11:10	Coffee and Posters	No Room Required
11:10 to 12:00	Yshai Avishai Ben-Gurion University Tight binding spectrum of electrons on the sphere, subject to the field of: I. Magnetic charge, II. Electric charge. A surprising relation between I. and II	No Room Required
12:00 to 12:50	Keith Slevin Osaka University Numerical estimates of critical exponents of the Anderson transition	No Room Required
12:50 to 14:30	Lunch and Discussion	No Room Required
14:30 to 15:20	Tomi Ohtsuki Sophia University Critical conductance distributions at the localization-delocalization transitions	No Room Required
15:20 to 16:10	tba	No Room Required
16:10 to 16:40	Tea and Posters	No Room Required
16:40 to 17:30	Hideo Aoki University of Tokyo Quantum hall effect and real-space wavefunctions --- multifractality and edge states in 2DEG and lattice systems	No Room Required
17:30 to 19:00	Discussions	No Room Required
19:00 to 20:00	Dinner	No Room Required

Wednesday 5th November 2008
09:00 to 09:50	Pierre Le Doussal CNRS - Ecole Normale Superieure Paris Some applications of freezing transitions	No Room Required
09:50 to 10:40	Yan Fyodorov Queen Mary University of London Random potentials with logarithmic correlations: multifractality of Boltzmann-Gibbs weights and extreme value statistics	No Room Required
10:40 to 11:10	Coffee and Posters	No Room Required
11:10 to 12:00	Stochastic scale invariance and KPZ equation	No Room Required
12:00 to 12:50	Oleg Yevtushenko Ludwig-Maximilians-Universität München Delocalization transition in unconventional random matrices	No Room Required
12:50 to 14:30	Lunch and Discussion	No Room Required
14:30 to 15:20	Eduardo Mucciolo University of Central Florida Universal vs. nonuniversal scaling of the conductivity in disordered graphene	No Room Required
15:20 to 16:10	Peter Markoš Slovak Academy of Sciences Universality of Anderson transition in disordered systems	No Room Required
16:10 to 16:40	Tea and Posters	No Room Required
16:40 to 17:30	Alexander Ossipov University of Nottingham Multifractality in delay times statistics	No Room Required
17:30 to 19:00	Discussions	No Room Required
19:00 to 20:00	Dinner	No Room Required

Thursday 6th November 2008
09:00 to 09:50	Vladimir Yudson Pereslavl-Zalessky of the Russian Academy of Sciences One-dimensional Anderson model: devil's staircase of statistical anomalies	No Room Required
09:50 to 10:40	Rodolf Roemer University of Warwick Multifractal analysis of the metal-insulator transition in the 3D Anderson model	No Room Required
10:40 to 11:10	Coffee and Posters	No Room Required
11:10 to 12:00	Imre Varga Budapest University of Technology and Economics Power-law banded random matrices: a testing ground for the Anderson transition	No Room Required
12:30 to 13:30	Lunch	No Room Required

Speakers

Hideo Aoki University of Tokyo
Yshai Avishai Ben-Gurion University
John Chalker University of Oxford
Ferdinand Evers
Mikhail Feigelman L.D.Landau Institute for Theoretical Physics, Moscow
Akira Furusaki RIKEN
Yan Fyodorov Brunel University
Illya Gruzberg University of Chicago
Victor Kagalovsky Sami Shamoon College of Engineering, Beer-Sheva, Israel
Vladimir Kravtsov Abdus Salam International Centre for Theoretical Physics
Pierre Le Doussal CNRS - Ecole Normale Superieure Paris
Peter Markoš Slovak Academy of Sciences
Alexander Mirlin
Eduardo Mucciolo University of Central Florida
Christopher Mudry
Hideaki Obuse Kyoto University
Tomi Ohtsuki Sophia University
Alexander Ossipov University of Nottingham
Rodolf Roemer University of Warwick
Keith Slevin Osaka University
Imre Varga Budapest University of Technology and Economics
Oleg Yevtushenko Ludwig-Maximilians-Universität München
Vladimir Yudson Pereslavl-Zalessky of the Russian Academy of Sciences

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Delocalization transition and multifractality

Workshop theme

Timetable

Speakers

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