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arXiv · 1511.05922

Time and temperature-dependent correlation function of an impurity in a one-dimensional Fermi gas as a Fredholm determinant

O. Gamayun·Andrei G. Pronko·Mikhail B. Zvonarev
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Abstract

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 [Nucl. Phys. B 892, 83 (2015)], and for arbitrary temperature and infinite repulsion in [Nucl. Phys. B 520, 594 (1998)].

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O. Gamayun, Andrei G. Pronko, Mikhail B. Zvonarev. 2015-11-18. Time and temperature-dependent correlation function of an impurity in a one-dimensional Fermi gas as a Fredholm determinant. https://doi.org/10.1088/1367-2630%2F18%2F4%2F045005

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