Abstract.
For rather general thermodynamic equilibrium distribution functions the density of a statistical ensemble of quantum mechanical particles depends analytically on the potential in the Schrödinger operator describing the quantum system. A key to the proof is that the resolvent to a power less than one of an elliptic operator with non-smooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to three-dimensional Lipschitz domain boundedly maps the space of square integrable functions to the space of essentially bounded functions.
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Communicated by Jean Bellissard & Joel Feldman.
Dedicated to Günter Albinus
Submitted: November 21, 2008. Accepted: March 31, 2009.
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Hoke, K., Kaiser, HC. & Rehberg, J. Analyticity for Some Operator Functions from Statistical Quantum Mechanics. Ann. Henri Poincaré 10, 749–771 (2009). https://doi.org/10.1007/s00023-009-0419-7
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DOI: https://doi.org/10.1007/s00023-009-0419-7