Diamagnetic currents
type: Item
instance of: scholarly article
title: Diamagnetic currents
zbMATH Open document ID: 0642.60106
DOI: 10.1007/BF01223591
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: We study the diamagnetic surface currents of particles in thermal equilibrium submitted to a constant magnetic field. The current density of independent electrons with Boltzmann (respectively Fermi) statistics has a Gaussian (respectively exponential) bound for its fall off into the bulk. For a system of interacting particles at low activity with Boltzmann statistics, the current density is localized near to the boundary and integrable when the two-body potential decays as \(| x|^{-\alpha}\), \(\alpha >4\), in three dimensions. In all cases, the integral of the current density is independent of the nature of the confining wall and correctly related to the bulk magnetisation. The results hold for hard and soft walls and all field strength. The analysis relies on the Feynman-Kac-Itô representation of the Gibbs state and on specific properties of the Brownian bridge process.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 4046870
zbMATH Keywords: thermal equilibrium
zbMATH Keywords: interacting particles
zbMATH Keywords: Boltzmann statistics
zbMATH Keywords: Feynman-Kac-Itô representation
zbMATH Keywords: Gibbs state
zbMATH Keywords: Brownian bridge process
author: Nicolas Macris
author: Philippe A. Martin
author: Joe V. Pulé
MaRDI profile type: Publication
cites work: Reduced Density Matrices of Quantum Gases. I. Limit of Infinite Volume
cites work: Q3872705
cites work: Q3910965
cites work: Bounds on Green’s functions of second-order differential equations
full work available at URL: https://doi.org/10.1007/bf01223591
OpenAlex ID: W4241129941
description: scientific article; zbMATH DE number 4046870