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arXiv:cond-mat/0011313 · International Journal of Modern Physics B

ROTATING FERMIONS IN TWO DIMENSIONS: A THOMAS–FERMI APPROACH

Sankalpa Ghosh, M. V. N. Murthy, Subhasis Sinha

Published Aug 10, 2001• 0 citations
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Abstract

Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy functional for a finite fermionic system within the Thomas–Fermi approximation in two dimensions. We show that for specific interactions the problem may be exactly solved. We derive analytical expressions for the density, the critical size as well as the ground state energy of such systems in a given angular momentum sector.

DOI
10.1142/s0217979201006549

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We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.
We investigate the angular momentum of a two-dimensional non-interacting Fermi gas confined in a rotating harmonic trap. By employing a quantum statistical approach, analytical expressions for the angular momentum are derived and analyzed as functions of particle number and rotation frequency. The rotational motion introduces a shell structure in the energy spectrum, giving rise to oscillatory behavior analogous to the de Haas–van Alphen oscillations observed in electronic systems subjected to magnetic fields. Numerical calculations reveal that these oscillations are most pronounced for weak rotation and small particle numbers, while they become progressively damped as the particle number increases. The results emphasize the close analogy between ultracold rotating gases and charged particles in magnetic fields and provide further insight into quantum rotational effects in confined Fermi systems.
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