Objective
This research programme will focus on the following topics: quantum groups and quantum algebras; description of new symmetries of physical systems; general structure, representations, geometrical aspects of quantum algebras; conformal field theory; perturbed conformal field theory; conformal field theory with infinite-dimensional symmetry algebras; statistical description of integrable systems; 'integrable turbulence'; the Hubbard model and its generalisations; non-linear optics; solitons in non-linear media; and quantum optics.
In the field of quantum groups and quantum algebras novel applications of q-algebra techniques to problems in condensed matter physics (generalized Hubbard model with phonons) and quantum optics (deformed Jaynes-Cummings model and its generalization) will be investigated. The connection between quantum algebras and aspects of non-commutative geometry will be studied, with special attention to how this geometrical interpretation bears on applications.
Theories close to conformal field theories, in the sense that their action may be reduced to the sum of a conformal invariant part plus a small non-invariant part, will be dealt with perturbatively. Conformal field theories endowed with a more extended symmetry (either dynamical or global) will be studied in the case when the additional symmetry is infinite dimensional (e.g. Kac-Moody or Virasoro).
The statistical description of integrable systems will be analyzed based on the notion of conformal 2-d turbulence and the ensuing relation with the Ising model in 3-d, the question of integrability in turbulence. The generalized Hubbard model and its supersymmetric realization recently proposed by V. Korepin and coworkers will be investigated, with the aim of constructing both reliable mean-field solutions and an exact ground state. The relevance of these models for high-Tc superconductivity will be discussed.
Several models characteristic of both non-linear and quantum optics have been recently reformulated in an algebraic setting which opens up the perspective that they may indeed be integrable. These models will be studied from this particular point of view.
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Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
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Funding Scheme
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Coordinator
10133 TORINO (TURIN)
Italy
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