Services aux conférences Mandl

Résumé: 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 ?-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.

Résumé: Quantum computing represents the prodigiously fertile union of quantum physics with the theory of computation and especially issues of computational complexity. It is known that quantum processes can offer solutions to some information processing tasks that are exponentially more efficient than any known classical methods. Perhaps the most celebrated example is Shor's 1994 quantum algorithm for integer factorisation.

In recent years there has been a surge of activity in our understanding of quantum computational power and its prospective applicability and limitations. A variety of problems in diverse areas of mathematics, has been identified (so-called BQP-complete problems) that have efficient quantum algorithms and also embody the full power of efficient quantum computation. In quantum many body physics (including study of quantum circuits, of local hamiltonians, and of further formalisms such as measurement based computing) some problems have been shown, surprisingly, to admit efficient classical solution while others (e.g. certain ground state properties of local hamiltonians) are likely to be computationally intractible, having been shown to be so-called QMA-complete. Quantum entanglement is often regarded as an essential ingredient in these considerations and there has been considerable development in understanding its scaling behaviour in many body systems.

This conference is devoted to recent theoretical developments in these areas and related issues. Invited speakers will be requested to include overview material (in addition to recent research) with the aim of making the essential ideas of these important developments accessible to a broader audience of QIP researchers.