×

Diamagnetic expansions for perfect quantum gases II: Uniform bounds. (English) Zbl 1154.82302

Summary: Consider a charged, perfect quantum gas, in the effective mass approximation, and in the grand-canonical ensemble. We prove in this paper that the generalized magnetic susceptibilities admit the thermodynamic limit for all admissible fugacities, uniformly on compacts included in the analyticity domain of the grand-canonical pressure.
The problem and the proof strategy were outlined in [P. Briet, H. D. Cornean and D. Louis, Markov Process. Relat. Fields 11, No. 2, 177–188 (2005; Zbl 1072.82004), P. Briet, H. D. Cornean and D. Louis, J. Math. Phys. 47, No. 8, 083511, 25 p. (2006; Zbl 1112.82003)] we proved in detail the pointwise thermodynamic limit near \(z=0\). The present paper is the last one of this series, and contains the proof of the uniform bounds on compacts needed in order to apply Vitali’s convergence theorem.

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
35Q40 PDEs in connection with quantum mechanics
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
PDFBibTeX XMLCite
Full Text: DOI arXiv