Objective
Quantum mechanical systems are quite often reflecting the underlying classical Hamiltonian structure of coordinate and phase space. This is the subject of semi-classical analysis. The tool for it is microlocal analysis. This project will continue and extend this development.
Semi-classical analysis of models of the Hofstadter type became a scientific tool for studying properties of charge transport in solid in the presence of a magnetic field. Interest in this area was boosted by the discovery of the Quantum Hall effect and the possibility to realise very small structures in large magnetic fields. These models are interesting also from several points of views. In particular there is an interesting connection to integrable models and quantum groups. They are a paradigm for a large area of interesting asymptotic problems in solid state physics to be explored further in this project. The methods to analyze Schrödinger operators for this class of models are microlocal analysis, complex WKB as well as C-star algebraic.
Microlocal analysis and its application to problems in quantum mechanics extends existing scientific co-operation by working in particular on the following subjects: semi-classical analysis of Schrödinger operators, pseudo-differential operators and applications to quantum mechanics, asymptotic methods in solid state physics, Schrödinger operators with periodic potentials, soluble models in the theory of non-linear partial differential equations, symplectic geometry and quantum mechanics, scattering theory and asymptotic methods.
Most of the work is analytic. However, in many cases it will be profitable to support mathematical analysis by computer graphics and number crunching.
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Programme(s)
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Topic(s)
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Funding Scheme
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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.