Levy distribution in many-particle quantum systems

Details Levy distribution in many-particle quantum systems Levy distribution in many-particle quantum systems

2009-07-24

arxiv.org/abs/0907.4328v4

Phys. Rev. A 81, 043615 (2010)

Physics

Condensed Matter

Quantum Gases

7 pages, 6 figures, results are generalized, new examples are added

Scientific paper

10.1103/PhysRevA.81.043615

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 $N$ 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.

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