Quantum dynamics of a mobile impurity in a one-dimensional Fermi gas
Oleksandr Gamayun (Leiden Unversity, The Netherlands)
A single impurity particle in an ultracold atomic gas is a prospective model for probing relaxation dynamics of an interacting out-of-equilibrium quantum system. I will focus on a case of an impurity that propagates in a one-dimensional gas of free fermions and interacts with them through the contact interaction. It is the simplest and yet fundamental model capturing a peculiar physics and mathematics of the non-equilibrium processes. A particular feature of this model is integrable when masses of the impurity and gas particles are equal. In this case, I will present a full nonpertubative solution and express physical quantities in terms of the Fredholm determinants of integrable integral operators. After a detailed analysis of the mathematical structure of the Fredholm determinants, I will discuss several striking physical phenomena such as incomplete relaxation, Bloch oscillations, and momentum-dependent impurity statistics. To describe the non-integrable case, I will develop a kinetic theory approach. I will then present its modification that allows description of the integrable case as well. Finally, I will give some arguments about the persistence of the discussed phenomena at a finite temperature.