WIAS Preprint No. 1373, (2008)

Analyticity for some operator functions from statistical quantum mechanics


  • Hoke, Kurt
  • Kaiser, Hans-Christoph
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 81Q10 35J10 35P20

2008 Physics and Astronomy Classification Scheme

  • 31.15.bt


  • Schrödinger operator, analyticity of operator functions, statistical ensemble of quantum systems, quantum mechanical particle density in many particle systems


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 factorizes over the space of essentially bounded functions.

Appeared in

  • Ann. Henri Poincare, 10 (2009) pp. 749--771.

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