Exact ground state number fluctuations of trapped ideal and interacting fermions

Details Exact ground state number fluctuations of trapped ideal and interacting fermions Exact ground state number fluctuations of trapped ideal and interacting fermions

2002-08-16

arxiv.org/abs/math-ph/0208023v1

J. Phys. A: Math. Gen. 36, 961 (2003)

Physics

Mathematical Physics

13 pages, 6 figures

Scientific paper

10.1088/0305-4470/36/4/308

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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