Ground state energy of dilute Bose gases in 1D

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We study the ground state energy of a gas of 1D bosons with density ρ, interacting through a general, repulsive 2-body potential with scattering length a, in the dilute limit ρ|a|≪1. The first terms in the expansion of the thermodynamic energy density are π2ρ3/3(1+2ρa), where the leading order is the 1D free Fermi gas. This result covers the Tonks-Girardeau limit of the Lieb-Liniger model as a special case, but given the possibility that a>0, it also applies to potentials that differ significantly from a delta function. We include extensions to spinless fermions and 1D anyonic symmetries, and discuss an application to confined 3D gases.
Antal sider36
StatusUdgivet - 2022

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