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