Ground state fluctuations in finite Fermi and Bose systems

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, when compared with canonical ensemble averaging, gives considerably different results, specially for fermions. This difference is expected to persist at low excitation even when the fermion number in the trap is large. PACS numbers: 05.40, 05.30.F, 05.30.J, 03.75.F Typeset using REVTEX ∗Permanant Address; The Institute of Mathematical Sciences, CIT Campus, Chennai 600 113, India