Development and applications of asymptotic and spectral methods for analysis of quantum systems

Información del proyecto

Identificador del acuerdo de subvención: INTAS-RFBR95-0414

Fecha de inicio

Fecha de finalización

Financiado con arreglo a

• International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993-

Coste total

Sin datos

Aportación de la UE

Sin datos

Coordinado por

Technische Universität Berlin
Germany

Objetivo

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.

Ámbito científico (EuroSciVoc)

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Programa(s)

• IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993-

Tema(s)

• 2 - Mathematics, Telecommunications, Information Technologies

Convocatoria de propuestas

Datos no disponibles

Régimen de financiación

Datos no disponibles

Coordinador

Technische Universität Berlin

• Aportación de la UE: Sin datos
• Dirección: 10623 Berlin ; Alemania
• Coste total: Sin datos

Participantes (1)

St. Petersburg State University

Rusia

• Aportación de la UE: Sin datos
• Dirección: 198904 St. Petersburg
• Coste total: Sin datos