Oleksandr Gamayun, Oleg Lychkovskiy, Mikhail B. Zvonarev
SciPost Phys. 8, 053 (2020) ·
published 7 April 2020

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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 TonksGirardeau bosons in one spatial dimension. We obtain a Fredholm determinant representation of the distribution function for the Bethe ansatz solvable model of an impuritygas δfunction 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 (quasicondensate) 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 onedimensional impenetrable anyons.
SciPost Phys. 8, 036 (2020) ·
published 5 March 2020

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We consider an integrable system of two onedimensional fermionic chains
connected by a link. The hopping constant at the link can be different from
that in the bulk. Starting from an initial state in which the left chain is
populated while the right is empty, we present timedependent full counting
statistics and the Loschmidt echo in terms of Fredholm determinants. Using this
exact representation, we compute the above quantities as well as the current
through the link, the shot noise and the entanglement entropy in the large time
limit. We find that the physics is strongly affected by the value of the
hopping constant at the link. If it is smaller than the hopping constant in the
bulk, then a local steady state is established at the link, while in the
opposite case all physical quantities studied experience persistent
oscillations. In the latter case the frequency of the oscillations is
determined by the energy of the bound state and, for the Loschmidt echo, by the
bias of chemical potentials.