The Absence Of Saturation Of The Level Number Variance In A Rectangular Box

Details The Absence Of Saturation Of The Level Number Variance In A Rectangular Box The Absence Of Saturation Of The Level Number Variance In A Rectangular Box

2003-06-04

arxiv.org/abs/cond-mat/0306110v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

15 pages, 4 figures

Scientific paper

The variance of the number of levels in an energy interval around a level with large quantum numbers (semiclassical quantization) is studied for a particle in a rectangular box. Sampling involves changing the ratio of the rectangle's sides while keeping the area constant. For sufficiently narrow intervals, one finds the usual linear growth with the width of the interval. For wider intervals, the variance undergoes large, non-decaying oscillations around what is expected to be the saturation value. These oscillations can be explained as a superposition of just a few harmonics that correspond to the shortest periodic orbits in the rectangle. The analytical and numerical results are in excellent agreement.

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