Oleg Lychkovskiy

Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas.

A kinetic theory describing the motion of an impurity particle in a degenerate Tonks-Girardeau gas is presented. The theory is based on the one-dimensional Boltzmann equation. An iterative procedure for solving this equation is proposed, leading to the exact solution in a number of special cases and to an approximate solution with the explicitly specified precision in a general case. Previously we reported that the impurity reaches a nonthermal steady state, characterized by an impurity momentum p(∞) depending on its initial momentum p(0) [E. Burovski, V. Cheianov, O. Gamayun, and O. Lychkovskiy, Phys. Rev. A 89, 041601(R) (2014)]. In the present paper the detailed derivation of p(∞)(p(0)) is provided. We also study the motion of an impurity under the action of a constant force F. It is demonstrated that if the impurity is heavier than the host particles, m(i)>m(h), damped oscillations of the impurity momentum develop, while in the opposite case, m(i)<m(h), oscillations are absent. The steady-state momentum as a function of the applied force is determined. In the limit of weak force it is found to be force independent for a light impurity and proportional to √[F] for a heavy impurity.

Momentum relaxation of a mobile impurity in a one-dimensional quantum gas

The motion of an impurity atom in a degenerate Tonks-Girardeau gas is investigated in the regime of weak impurity-host coupling. It is shown that given some initial momentum

Dependence of decoherence-assisted classicality on the way a system is partitioned into subsystems

p_0

Necessary condition for the thermalization of a quantum system coupled to a quantum bath.

an impurity relaxes to a steady state with a non-vanishing average momentum

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

p_\infty.

Reply to "Comment on 'Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas' ".

The function

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

p_\infty(p_0)

Quantum many-body adiabaticity, topological Thouless pump and driven impurity in a one-dimensional quantum fluid

is calculated explicitly in the limit of vanishing coupling constant. Further to this, an impurity driven by a weak constant force is shown to exhibit pronounced momentum oscillations in agreement with earlier theoretical predictions.

Spin dynamics in a finite cyclic X Y model

Choosing a specific way of dividing a closed system into parts is a starting point for the decoherence program and for the quantum thermalization program. It is shown that one can always choose a way of partitioning so that decoherence-assisted classicality does not emerge and thermalization does not occur. Implications of this result are discussed.

Squaring parametrization of constrained and unconstrained sets of quantum states

A system put in contact with a large heat bath normally thermalizes. This means that the state of the system ρS(t) approaches an equilibrium state ρ(eq)(S), the latter depending only on macroscopic characteristics of the bath (e.g., temperature) but not on the initial state of the system. The above statement is the cornerstone of the equilibrium statistical mechanics; its validity and its domain of applicability are central questions in the studies of the foundations of statistical mechanics. In the present paper we concentrate on one aspect of thermalization, namely, on the system initial state independence (ISI) of ρ(eq)(S). A necessary condition for the system ISI is derived in the quantum framework. We use the derived condition to prove the absence of the system ISI in a specific class of models. Namely, we consider a single spin coupled to a large bath, the interaction term commuting with the bath self-Hamiltonian (but not with the system self-Hamiltonian). Although the model under consideration is nontrivial enough to exhibit the decoherence and the approach to equilibrium, the derived necessary condition is not fulfilled and thus ρ(eq)(S) depends on the initial state of the spin.