High-momentum tail in the Tonks-Girardeau gas under general confining potentials

TL;DR

This paper proves that the ground state momentum distribution of a one-dimensional impenetrable boson system always has a $k^{-4}$ tail regardless of the confining potential, providing a universal feature and practical computation method.

Contribution

It establishes a universal $k^{-4}$ tail in the momentum distribution for the Tonks-Girardeau gas under any confining potential and derives a simple expression for asymptotic occupation numbers.

Findings

Universal $k^{-4}$ tail in momentum distribution

Derived an expression for asymptotic occupation numbers

Validated results with exact numerical methods

Abstract

We prove that the ground state momentum distribution of a one-dimensional system of impenetrable bosons exhibits a $k^{-4}$ tail for any confining potential. We also derive an expression for easily computing the asymptotic occupation numbers and verify our results with an exact numerical approach.