Diamagnetic expansions for perfect quantum gases II: Uniform bounds

Abstract

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 [3]. In [4] 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.

A rigorous approach to the magnetic response in disordered systems

“…Our paper is an extension of the works of Briet et al [3,4,5] where the case of a perfect quantum gas has been treated. All these papers are in fact in the continuation of a study initiated by Angelescu et al [1,2]; for a brief review see also [10,4].…”

A Rigorous Proof of the Landau-Peierls Formula and much more

“…Our current paper is based on what we call magnetic perturbation theory, as developed by the authors and their collaborators in a series of papers starting with 2000 (see [13,12,14,15,16,3,4,5,6,7] and references therein). The results we obtain in Theorem 1.2 give a complete answer to the problem of zero-field susceptibility.…”

“…One can see this by performing an integration by parts in (3.2) and using the fact that the kernel of R 2 ∞ (ω, ξ) is jointly continuous. Moreover, one can prove [4,5,6] that the thermodynamic limit of the grand-canonical pressure is jointly smooth on (z, ω) ∈ (−e βE0 , ∞) × R.…”

Gaussian decay for a difference of traces of the Schrödinger semigroup associated with the isotropic harmonic oscillator

“…The proof of Lemma 2.3 in the case of d = 3 can be found in [5,Lem. 4.2], see also [6]. Since the generalization to d = 1, 2 can be easily obtained by similar arguments, we do not give any proof.…”