Objective
Effective particles in external fields, many-electron systems and integrable models of statistical physics are now among the most complicated quantum systems actively investigated in many centers. Quite sophisticated mathematical methods, mostly, analytical ones (asymptotic and spectral) play an essential role in the analysis of such systems. The analysis and the quantum mechanics mutually stimulate each other in their interaction. The mathematical nature of the problems has many common with the mathematical nature of more classical problems of Mathematical Physics. The scientific groups proposing the project have long time recognized experience in the field. The concrete topics reflected in the project can be included in the list of actual problems of mathematical physics. The groups have already positive experiences of collaboration.
Research activities:
The main goals of the project: asymptotic analysis of operators with the singular spectrum, asymptotic and qualitative analysis of the spectrum of many-electron systems, asymptotic properties of correlation functions of integrable models of statistical physics, semiclassical pseudo-differential operators with discontinuous symbols, semiclassical analysis in applications to ODE and PDE, spectral analysis in large dimensions, asymptotic properties of the spectrum of Bloch electrons in external fields.
Main models: Hofstadter models, Tomas-Fermi model, quasi-relativisticmany-particle hamiltonians, Born-Oppenheimer approximation, many-particle systems in external fields, quantum integrable models in one-dimension, pseudodifferential operators with discontinuous symbols, scattering by obstacles, Bloch electrons in external fields.
Main tools: adiabatic approach, monodromization method, semiclassicalapproach, microlocal analysis, quantum inverse scattering method, Bethe anzatz, irreducible representations of operator algebras, qualitative spectral theory of differential operators, variational methods.
The results:
are assumed to be reflected by scientific publications.
Fields of science (EuroSciVoc)
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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.
Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
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Coordinator
10623 Berlin
Germany
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.