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

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 re…