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Journal of Experimental and Theoretical Physics Letters

Magnetic susceptibility of noninteracting fermions in a confined geometry

Arthur Minnullin, Tayurskii Dmitrii Albertovich

Published Dec 1, 2000• 6 citations
Publisher

Abstract

A model system of an ideal gas of neutral fermions in a confined geometry of different symmetry and size is theoretically examined. The behavior of these systems is found to exhibit qualitatively new features such as the oscillations in magnetic susceptibility with changing geometry size and particle density, indicating that the geometric confinement substantially affects the thermodynamic properties of the system.

DOI
10.1134/1.1351202

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A model system of an ideal gas of neutral fermions in a confined geometry of different symmetry and size is theoretically examined. The behavior of these systems is found to exhibit qualitatively new features such as the oscillations in magnetic susceptibility with changing geometry size and particle density, indicating that the geometric confinement substantially affects the thermodynamic properties of the system.
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We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin-polarized fermions in a confinement potential. This study is an extension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a three-dimensional model of N harmonically interacting spin-polarized fermions in a parabolic potential well in the presence of a magnetic field. The free energy and the internal energy are obtained for a limited number of particles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present in the well, scaling relations similar to those of the continuum approximation to the density of states are already satisfied.
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We discuss the spin fluctuations and the role played by the magnetic susceptibility in an atomic Fermi gas interacting with a positive scattering length. Both thermal and zero-temperature quantum fluctuations are considered. Using a sum rule approach and recent ab initio Monte Carlo results for the magnetic susceptibility of uniform matter, we provide explicit predictions for the frequency of the spin dipole oscillation of a gas trapped by a harmonic potential and discuss the deviations from the ideal gas behavior when the system approaches the ferromagnetic transition. The role of the Landau's parameters in the characterization of the magnetic properties is also discussed.
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The system we consider here is a charged fermions gas in the effective mass approximation, and in grand-canonical conditions. We assume that the particles are confined in a three dimensional cubic box ΛΛΛ with side L≥1L\geq 1L≥1, and subjected to a constant magnetic field of intensity $ B \geq 0 $. Define the grand canonical generalized susceptibilities χLNχ_L^NχLN​, N≥1N\geq 1N≥1, as successive partial derivatives with respect to BBB of the grand canonical pressure PLP_LPL​. Denote by P∞P_{\infty}P∞​ the thermodynamic limit of PLP_LPL​. Our main result is that χLNχ_L^NχLN​ admit as thermodynamic limit the corresponding partial derivatives with respect to BBB of P∞P_{\infty}P∞​. In this paper we only give the main steps of the proofs, technical details will be given elsewhere.