This interdisciplinary research proposal is intended to investigate under what circumstances the physics of the Anderson transition (localization-delocalisation transition characterized by multi-fractal wave functions and scale invariant spectrum) appears in (quantum chromodynamics) QCD and quantum chaos. Once these relations are established we plan to explore the possibility of translating the mathematical techniques developed in any of these fields to solve current standing problems in the other two fields. I n the context of QCD context we first propose a model of the QCD vacuum as based on disordered systems ideas. Then we show that de-confinement and the restoration of the chiral symmetry occurring at finite temperature share all the properties of a delocalisation-localization (Anderson) transition.
From a technical point of view we combine non-pertubative field theory techniques (instant on liquid models) with disordered systems (super-symmetry method) techniques. In the context of quantum chaos we show that a quantum system with classical counterpart presenting intermittency undergoes a quantum Anderson transition in a certain region of parameters.
Also we want to relate classical intermittency with certain universal non-analytical properties of the classical potential. These findings open new experimental ways to study both the Anderson transition and classical-quantum correspondence. The experience acquired in the first part of the fellowship will greatly (more than in any European institution) enhance the quality of the proposed research by stimulating his independent thinking, leadership and initiative. These benefits will have immediate impact on my research results during the second stage of the fellowship and beyond.
Call for proposal
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