Levy distribution in many-particle quantum systems
Abstract
Levy distribution, previously used to describe complex behavior of classical systems, is shown to characterize that of quantum many-body systems. Using two complimentary approaches, the canonical and grand-canonical formalisms, we discovered that the momentum profile of a Tonks-Girardeau gas, -- a one-dimensional gas of impenetrable (hard-core) bosons, harmonically confined on a lattice at finite temperatures, obeys Levy distribution. Finally, we extend our analysis to different confinement setups and demonstrate that the tunable Levy distribution properly reproduces momentum profiles in experimentally accessible regions. Our finding allows for calibration of complex many-body quantum states by using a unique scaling exponent.
Cite
@article{arxiv.0907.4328,
title = {Levy distribution in many-particle quantum systems},
author = {A. V. Ponomarev and S. Denisov and P. Hanggi},
journal= {arXiv preprint arXiv:0907.4328},
year = {2010}
}
Comments
7 pages, 6 figures, results are generalized, new examples are added