We investigate the momentum distribution function of a single distinguishable impurity particle which formed a polaron state 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 δ-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.
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- 1 Institute of Physics, University of Amsterdam [IoP, UvA]
- 2 Математический институт им. В. А. Стеклова / Steklov Mathematical Institute
- 3 Skolkovo Institute of Science and Technology [Skoltech]
- 4 Université Paris-Saclay / University of Paris-Saclay