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Delocalization Transition and Multifractality

2nd November 2008 to 6th November 2008

Organisers: Ferdinand Evers (Karlsruhe) and Yan Fyodorov (Nottingham)

Co-organised with the Karlsruhe Institute of Technology, Germany

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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.

multifractal wave function at the critical point

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)

University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons