Oleksandr Gamayun

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

Impurity Green's function of a one-dimensional Fermi gas

p_0

Time scale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe

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

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

p_infty.

Two-terminal transport along a proximity-induced superconducting quantum Hall edge

The function

Impact of the Injection Protocol on an Impurity’s Stationary State

p_infty(p_0)

Necessary and sufficient condition for quantum adiabaticity in a driven one-dimensional impurity-fluid system

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.

Breakdown of adiabaticity in a driven one-dimensional impurity-fluid system

Abstract We consider a one-dimensional gas of spin-1/2 fermions interacting through δ -function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point correlation function of the spin-down fermion. This impurity Greens function is represented in the thermodynamic limit as an integral of Fredholm determinants of integrable linear integral operators.

Two-terminal transport along a proximity induced quantum Hall edge

The adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what slowly enough means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely, many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter-dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving nonautonomous time evolution in a large Hilbert space.