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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 13: Offene Quantensysteme
MP 13.2: Talk
Thursday, March 1, 2012, 10:05–10:30, ZHG 003
Mappings of open quantum systems onto chain representations and Markovian embeddings — •M.P. Woods1,2, R. Groux3, A.W. Chin1, S.F. Huelga1, and M.B. Plenio1,2 — 1Institut für Theoretische Physik, Universität Ulm, D-89069 Ulm, Germany — 2QOLS, Blackett Laboratory, Imperial College London, SW7 2BW, United Kingdom — 3Lycee Polyvalent Rouviere, Rue Sainte Claire Deville. BP 1205, 83070 Toulon, France
This talk is concerned with the mapping of the Hamiltonian of open quantum systems onto chain representations, which forms the basis for a rigorous theory of the interaction of a system with its environment. This mapping progresses as an iteration which gives rise to a sequence of residual spectral densities whose properties determines the essential physical properties of the system. The rigorous mathematical properties of this mapping have been unknown so far. Here we develop the theory of secondary measures to derive an analytic, non-iterative expression for the sequence solely in terms of the initial measure and its associated orthogonal polynomials of the first and second kind. By formulating this new result in terms of a theory concerning Jacobi matrices, we find a very general connection between spectral theory and open quantum systems. These results make a significant and mathematically rigorous contribution to the understanding of the theory of open quantum systems, and paves the way towards the efficient simulation of these systems, which within the standard methods, is often an intractable problem.
A preprint is available here: http://arxiv.org/abs/1111.5262