One Dimensional Magnetized TG Gas Properties in an External Magnetic Field

TL;DR

This paper constructs eigenstates of a one-dimensional magnetized Tonks-Girardeau (TG) gas in an external magnetic field, analyzing its properties and comparing them with Fermi gases, revealing similarities and differences in various physical quantities.

Contribution

It introduces a method to construct eigenstates of a magnetized TG gas in a magnetic field and compares its properties with those of Fermi gases, highlighting new insights.

Findings

Ground state probability increases when N is commensurate with M.

Average particle coordinate and potential energy are similar to Fermi gas.

Reduced single-particle matrices and momentum distributions differ from Fermi gas.

Abstract

With Girardeau's Fermi-Bose mapping, we have constructed the eigenstates of a TG gas in an external magnetic field. When the number of bosons $N$ is commensurate with the number of potential cycles $M$, the probability of this TG gas in the ground state is bigger than the TG gas raised by Girardeau in 1960. Through the comparison of properties between this TG gas and Fermi gas, we find that the following issues are always of the same: their average value of particle's coordinate and potential energy, system's total momentum, single-particle density and the pair distribution function. But the reduced single-particle matrices and their momentum distributions between them are different.