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Zero temperature momentum distribution of an impurity in one-dimensional Fermi and Tonks-Girardeau gases | | Oleksandr Gamayun
; Oleg Lychkovskiy
; Mikhail B. Zvonarev
; | | Date: |
16 Sep 2019 | | Abstract: | We investigate the momentum distribution function of a single distinguishable
impurity particle immersed in a gas of either free fermions or Tonks-Girardeau
bosons in one spatial dimension. We obtain a Fredholm determinant
representation of the distribution function for the Bethe ansatz solvable model
of an impurity-gas $delta$-function interaction potential at zero temperature,
in both repulsive and attractive regimes. We deduce from this representation
the fourth power decay at a large momentum, and a weakly divergent
(quasi-condensate) peak at a finite momentum. We also demonstrate that the
momentum distribution function in the limiting case of infinitely strong
interaction can be expressed through a correlation function of the
one-dimensional impenetrable anyons. | | Source: | arXiv, 1909.7358 | | Services: | Forum | Review | PDF | Favorites | |
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