Savoie, Baptiste (2015) A rigorous proof of the Bohr–van Leeuwen theorem in the semiclassical limit. Reviews in Mathematical Physics, 27 (08). p. 1550019. ISSN 0129055X

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Abstract
The original formulation of the Bohrvan Leeuwen (BvL) theorem states that, in a uniform magnetic field and in thermal equilibrium, the magnetization of an electron gas in the classical DrudeLorentz model vanishes identically. This stems from classical statistics which assign the canonical momenta all values ranging from −∞ to ∞ what makes the free energy density magneticfieldindependent. When considering a classical (MaxwellBoltzmann) interacting electron gas, it is usually admitted that the BvL theorem holds upon condition that the potentials modeling the interactions are particlevelocitiesindependent and do not cause the system to rotate after turning on the magnetic field. From a rigorous viewpoint, when treating large macroscopic systems one expects the BvL theorem to hold provided the thermodynamic limit of the free energy density exists (and the equivalence of ensemble holds). This requires suitable assumptions on the manybody interactions potential and on the possible external potentials to prevent the system from collapsing or flying apart. Starting from quantum statistical mechanics, the purpose of this article is to give, within the linearresponse theory, a proof of the BvL theorem in the semiclassical limit when considering a dilute electron gas in the canonical conditions subjected to a class of translational invariant external potentials.
Item Type:  Article 

Uncontrolled Keywords:  Classical magnetism, Diamagnetism, Bohrvan Leeuwen Theorem, MaxwellBoltzmann statistics, Thermodynamic limit, Ensemble equivalence, Thermodynamic stability, Semiclassical limit, Geometric perturbation theory, Gauge invariant magnetic perturbation theory 
Divisions:  School of Theoretical Physics > Preprints 
Date Deposited:  05 Oct 2017 19:31 
Last Modified:  26 Jul 2018 10:38 
URI:  http://dair.dias.ie/id/eprint/322 
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