Perpetual motion of a mobile impurity in a one-dimensional quantum gas

Abstract

Consider an impurity particle injected in a degenerate one-dimensional (1D) gas of noninteracting fermions (or, equivalently, Tonks-Girardeau bosons) with some initial momentum p0. We examine the infinite-time value of the momentum of the impurity, p∞, as a function of p0. A lower bound on |p∞(p0)| is derived under fairly general conditions. The derivation, based on the existence of the lower edge of the spectrum of the host gas, does not resort to any approximations. The existence of such bound implies the perpetual motion of the impurity in a one-dimensional gas of noninteracting fermions or Tonks-Girardeau bosons at zero temperature. The bound admits an especially simple and useful form when the interaction between the impurity and host particles is everywhere repulsive.

Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid

“…In the context of ultracold-atom experiments, this potential is an excellent low-energy approximation to any real impurity-fluid coupling with positive scattering length a, with Uo being a function of a and transverse confinement energy [26]. This result has been obtained earlier for a special case of an impurity in a ID gas of free fermions [9]; here it is proven for an arbitrary interacting ID fluid.…”

“…This constitutes the major advancement over recent works [7,9,[13][14][15][16][17]19,20] focused on ID fluids which explicitly invoked special features of physics in one dimension.…”

Time and temperature-dependent correlation function of an impurity in one-dimensional Fermi and Tonks–Girardeau gases as a Fredholm determinant

“…However, the form-factors summation (which we do analytically in section 6 for the impurity correlation function) was done numerically in [15]. Later, the same problem was addressed with other techniques [36][37][38][39][40]. The existing results were obtained for particular time scales (for example, short time in the case of simulations using time-dependent density matrix renormalization group) and values of the external parameters (for example, weak impurity-gas coupling in the case of calculations done by diagrammatic methods).…”

Entanglement-assisted tunneling dynamics of impurities in a double well immersed in a bath of lattice trapped bosons

“…Indeed, in these systems correlation effects, such as entanglement, are expected to be a crucial ingredient since the impurities form a few-body subsystem [47]. Moreover, the underlying trapping potential plays an important role for the behavior of the impurity species, which has been analyzed for homogeneous systems [48][49][50], harmonic confinements [51][52][53][54][55] as well as lattice potentials [33,56,57]. The majority of the above-mentioned investigations have been focusing on the case where both species are trapped in the same geometry.…”