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Nuclear Physics B

Correlation function of the one-dimensional fermi gas in the infinite-coupling limit (repulsive case)

Alexander Bérkovich, J. H. Lowenstein

Published Jan 1, 1987• 25 citations
Publisher
DOI
10.1016/0550-3213(87)90329-4

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We investigate a free one-dimensional spinless Fermi gas, and the Tonks–Girardeau gas interacting with a single impurity particle of equal mass. We obtain a Fredholm determinant representation for the time-dependent correlation function of the impurity particle. This representation is valid for an arbitrary temperature and an arbitrary repulsive or attractive impurity-gas δ -function interaction potential. It includes, as particular cases, the representations obtained for zero temperature and arbitrary repulsion in (Gamayun et al 2015 Nucl. Phys. B 892 83–104 ), and for arbitrary temperature and infinite repulsion in (Izergin and Pronko 1998 Nucl. Phys. B 520 594–632 ).
The thermodynamic properties for a gas of one-dimensional fermi particles interacting via a repulsive delta-function potential have been studied under the limit of infinite repulsive coupling using the theory of grand canonical ensemble. All the thermodynamic functions have been found explicitly and the velocity of sound is derived as a function of the fugacity. In particular, the entropy is not zero at the absolute zero temperature for this model. Finally, some results are given for the arbitrary spin gas.