Levy distribution in many-particle quantum systems

TL;DR

This paper demonstrates that Levy distribution accurately describes the momentum profiles of quantum many-body systems, specifically a Tonks-Girardeau gas, across various confinement setups, enabling state calibration via a scaling exponent.

Contribution

It introduces the application of Levy distribution to quantum many-body systems and extends its use to different confinement setups for experimental relevance.

Findings

Levy distribution characterizes the momentum profile of a Tonks-Girardeau gas.

The approach applies to various confinement configurations.

Momentum profiles can be calibrated using a tunable Levy distribution.

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 $N$ 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.