Mobile impurity in a one-dimensional gas at finite temperatures

Oleksandr Gamayun, Miłosz Panfil, and Felipe Taha Sant'Ana
Phys. Rev. A 106, 023305 – Published 5 August 2022

Abstract

We consider the McGuire model of a one-dimensional gas of free fermions interacting with a single impurity. We compute the static one-body function and momentum distribution of the impurity at finite temperatures. The results involve averages over Fredholm determinants that we further analyze using the effective form factors approach. With this approach, we derive the large-distance behavior of the one-body function, which takes the form of an averaged exponential decay. This method allows us to study an experimentally important regime of small momenta of the impurity's momentum distribution. We also consider the one-body function at short distances and compute finite-temperature Tan's contact.

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  • Received 25 February 2022
  • Accepted 7 July 2022

DOI:https://doi.org/10.1103/PhysRevA.106.023305

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & OpticalStatistical Physics & Thermodynamics

Authors & Affiliations

Oleksandr Gamayun*

  • Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland and Bogolyubov Institute for Theoretical Physics, 03143 Kyiv, Ukraine

Miłosz Panfil and Felipe Taha Sant'Ana

  • Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland

  • *Corresponding author: oleksandr.gamayun@fuw.edu.pl

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Issue

Vol. 106, Iss. 2 — August 2022

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