August 16, 2002

Muoi N. Tran

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.

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We consider a small and fixed number of fermions (bosons) in a trap. The ground state of the system is defined at T=0. For a given excitation energy, there are several ways of exciting the particles from this ground state. We formulate a method for calculating the number fluctuation in the ground state using microcanonical counting, and implement it for small systems of noninteracting fermions as well as bosons in harmonic confinement. This exact calculation for fluctuation, ...

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We consider a fixed number of noninteracting bosons in a harmonic trap. The determination of the exact microcanonical ground state number fluctuation is a difficult enterprise. There have been several theoretical attempts to solve this problem approximately, especially in 1D models where analytic results were found using some asymptotic formulae from number theory. Here, we obtain the exact number fluctuation curves, and show that these exact curves are substantially differen...

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R. K. Bhaduri, M. V. N. Murthy, Muoi N. Tran

It is well-known that the number fluctuation in the grand canonical ensemble, which is directly proportional to the compressibility, diverges for an ideal bose gas as T -> 0. We show that this divergence is removed when the atoms interact in one dimension through an inverse square two-body interaction. In two dimensions, similar results are obtained using a self-consistent Thomas-Fermi (TF) model for a repulsive zero-range interaction. Both models may be mapped on to a system...

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