Level shift operators for open quantum systems |
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Authors: | Marco Merkli |
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Institution: | Department of Mathematics and Statistics, McGill University, 805 Sherbrooke W., Montreal, Canada, QC H3A 2K6 Centre de Recherches Mathématiques, Université de Montréal, Succursale Centre-Ville, Montréal, Canada, QC H3C 3J7 |
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Abstract: | Level shift operators describe the second-order displacement of eigenvalues under perturbation. They play a central role in resonance theory and ergodic theory of open quantum systems at positive temperatures. We exhibit intrinsic properties of level shift operators, properties which stem from the structure of open quantum systems at positive temperatures and which are common to all such systems. They determine the geometry of resonances bifurcating from eigenvalues of positive temperature Hamiltonians and they relate the Gibbs state, the kernel of level shift operators, and zero energy resonances. We show that degeneracy of energy levels of the small part of the open quantum system causes the Fermi Golden Rule Condition to be violated and we analyze ergodic properties of such systems. |
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Keywords: | Open quantum systems Thermal quantum field Quantum resonances Ergodic theory Fermi Golden Rule Complex deformation KMS states Tomita-Takesaki theory von Neumann algebra |
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