Exact ground state number fluctuations of trapped ideal and interacting fermions

Abstract

We consider a small and fixed number of fermions in an isolated one-dimensional trap (microcanonical ensemble). The ground state of the system is defined at T=0, with the lowest single-particle levels occupied. The number of particles in this ground state fluctuates as a function of excitation energy. By breaking up the energy spectrum into particle and hole sectors, and mapping the problem onto the classic number partitioning theory, we formulate a new method to calculate the exact particle number fluctuation more efficiently than the direct combinatorics method. The exact ground state number fluctuation for particles interacting via an inverse-square pair-wise interaction is also calculated.

13 pages, 6 figures

References in corpus (4)

• Canonical Statistics of Trapped Ideal and Interacting Bose Gases
• Statistical Properties of Interacting Bose Gases in Quasi-2D Harmonic Traps
• Number Fluctuation in an interacting trapped gas in one and two dimensions
• Exclusion Statistics in a two-dimensional trapped Bose gas

Cited by in corpus (5)

• On the Quantum Density of States and Partitioning an Integer
• Fermi-Dirac statistics and the number theory
• Thermodynamics of low-dimensional trapped Fermi gases
• Condensation in ideal Fermi gases
• Number Fluctuation and the Fundamental Theorem of Arithmetic