Number Fluctuation and the Fundamental Theorem of Arithmetic

Details Number Fluctuation and the Fundamental Theorem of Arithmetic Number Fluctuation and the Fundamental Theorem of Arithmetic

2002-10-28

arxiv.org/abs/cond-mat/0210624v1

Phys. Rev. E 68, 026105 (2003)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures. To be submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevE.68.026105

We consider N bosons occupying a discrete set of single-particle quantum states in an isolated trap. Usually, for a given excitation energy, there are many combinations of exciting different number of particles from the ground state, resulting in a fluctuation of the ground state population. As a counter example, we take the quantum spectrum to be logarithms of the prime number sequence, and using the fundamental theorem of arithmetic, find that the ground state fluctuation vanishes exactly for all excitations. The use of the standard canonical or grand canonical ensembles, on the other hand, gives substantial number fluctuation for the ground state. This difference between the microcanonical and canonical results cannot be accounted for within the framework of equilibrium statistical mechanics.

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