Lack of thermalization for integrability-breaking impurities

We employ equation of motion techniques to study the non-equilibrium dynamics in a lattice model of weakly interacting spinless fermions. Our model provides a simple setting for analyzing the effects of weak integrability breaking perturbations on the time evolution after a quantum quench. We establish the accuracy of the method by comparing results at short and intermediate times to time-dependent density matrix renormalization group computations. For sufficiently weak integ...

Eigenstate thermalization is widely accepted as the mechanism behind thermalization in generic isolated quantum systems. Using the example of a single magnetic defect embedded in the integrable spin-1/2 $XXZ$ chain, we show that locally perturbing an integrable system can give rise to eigenstate thermalization. Unique to such setups is the fact that thermodynamic and transport properties of the unperturbed integrable chain emerge in properties of the eigenstates of the pertur...

We investigate the effect on the entanglement dynamics of an impurity moving at constant velocity in a closed quantum system. We focus on one-dimensional strongly-correlated lattice models, both in the presence of integrable and chaotic dynamics. In the former, the slow impurity is preceded by fast quasiparticles carrying an "endogenous" entanglement front which decays in time as a power-law; on the contrary, a fast impurity drags itself an "exogenous" entanglement front whic...

A plausible mechanism of thermalization in isolated quantum systems is based on the strong version of the eigenstate thermalization hypothesis (ETH), which states that all the energy eigenstates in the microcanonical energy shell have thermal properties. We numerically investigate the ETH by focusing on the large deviation property, which directly evaluates the ratio of athermal energy eigenstates in the energy shell. As a consequence, we have systematically confirmed that th...

Impurity motion in one dimensional ultra cold quantum liquids confined in an optical trap has attracted much interest recently. As a step towards its full understanding, we construct a generating functional from which we derive the position non equilibrium correlation function of a quantum Brownian particle with general Gaussian non-factorizing initial conditions. We investigate the slow dynamics of a particle confined in a harmonic potential after a position measurement; the...

The long-time dynamics of quantum systems, typically, but not always, results in a thermal steady state. The microscopic processes that lead to or circumvent this fate are of interest, since everyday experience tells us that not all spatial regions of a system heat up or cool down uniformly. This motivates the question: under what conditions can one slow down or completely arrest thermalization locally? Is it possible to construct realistic Hamiltonians and initial states suc...

We develop a microscopic theory of a quantum impurity propagating in a one-dimensional Bose liquid. As a result of scattering off thermally excited quasiparticles, the impurity experiences the friction. We find that, at low temperatures, the resulting force scales either as the fourth or the eighth power of temperature, depending on the system parameters. For temperatures higher than the chemical potential of the Bose liquid, the friction force is a linear function of tempera...

The dynamics of an active, finite-size and immiscible impurity in a dilute quantum fluid at finite temperature is characterized by means of numerical simulations of the projected Gross--Pitaevskii equation. The impurity is modeled as a localized repulsive potential and described with classical degrees of freedom. It is shown that impurities of different sizes thermalize with the fluid and undergo a stochastic dynamics compatible with an Ornstein--Uhlenbeck process at sufficie...

Nonintegrability is a necessary condition for the thermalization of a generic Hamiltonian system. In practice, the integrability can be broken in various ways. As illustrating examples, we numerically studied the thermalization behaviors of two types of one-dimensional (1D) diatomic chains in the thermodynamic limit. One chain was the diatomic Toda chain whose nonintegrability was introduced by unequal masses. The other chain was the diatomic Fermi-Pasta-Ulam-Tsingou-$\beta$ ...

We study the thermal properties of impurities embedded in a repulsive Bose gas under a harmonic trapping potential. In order to obtain exact structural properties in this inhomogeneous many-body system, we resort to the path-integral Monte Carlo method. We find that, at low temperatures, a single impurity is expelled to the edges of the bath cloud if the impurity-boson coupling constant is larger than the boson-boson one. However, when the temperature is increased, but still ...