Off-equilibrium scaling driven by time-dependent external fields in O(N) vector-models.

We investigate the off-equilibrium dynamics of spin systems with O(N) symmetry arising by the presence of slowly varying time-dependent external fields. We show the general theory and then focus on two different cases: a time-dependent magnetic field h(t,ts) ≈ t/ts, ts is a time scale, at the critical temperature and the temperature deviations T (t, ts )/Tc − 1 ≈ −t/ts in the absence of magnetic fields. We demonstrate the off-equilibrium scaling behaviours and formally compute the correlation functions in the limit of large N. We study the first deviations from the equilibrium in the correlation functions and prove that the matching occurs exponentially fast. We also consider analogous phenomena at the first-order transition which occurs in the ordered phase T < Tc along the line of zero magnetic field

Out-of-equilibrium scaling behavior arising during round-trip protocols across a quantum first-order transition

We investigate the nonequilibrium dynamics of quantum spin chains during a round-trip protocol that slowly drives the system across a quantum first-order transition. Out-of-equilibrium scaling behaviors \`a la Kibble-Zurek for the single-passage protocol across the first-order transition have been previously determined. Here, we show that such scaling relations persist when the driving protocol is inverted and the transition is approached again by a far-from-equilibrium state. This results in a quasi-universality of the scaling functions, which keep some dependence on the details of the protocol at the inversion time. We explicitly determine such quasi-universal scaling functions by employing an effective two-level description of the many-body system near the transition. We discuss the validity of this approximation and how this relates to the observed scaling regime. Although our results apply to generic systems, we focus on the prototypical example of a $1D$ transverse field Ising model in the ferromagnetic regime, which we drive across the first-order transitions through a time-dependent longitudinal field.Comment: 13 pages, 18 figures; v2: minor changes; fixed some typo

Exact solution of time-dependent Lindblad equations with closed algebras

Time-dependent Lindblad master equations have important applications in areas ranging from quantum thermodynamics to dissipative quantum computing. In this paper we outline a general method for writing down exact solutions of time-dependent Lindblad equations whose superoperators form closed algebras. We focus on the particular case of a single qubit and study the exact solution generated by both coherent and incoherent mechanisms. We also show that if the time-dependence is periodic, the problem may be recast in terms of Floquet theory. As an application, we give an exact solution for a two-levels quantum heat engine operating in a finite-time.Comment: 15 pages, 12 figure

Entanglement dynamics of a hard-core quantum gas during a Joule expansion

We study the entanglement dynamics of a one-dimensional hard-core quantum gas initially confined in a box of size $L$ with saturated density $\rho=1$. The gas is suddenly released into a region of size $2L$ by moving one of the box edges. We show that the analytic prediction for the entanglement entropy obtained from quantum fluctuating hydrodynamics holds quantitatively true even after several reflections of the gas against the box edges. We further investigate the long time limit $t/L\gg 1$ where a Floquet picture of the non-equilibrium dynamics emerges and hydrodynamics eventually breaks down.Comment: 24 pages, 15 figure

Navier-Stokes equations for low-temperature one-dimensional fluids

We consider one dimensional interacting quantum fluids, such as the Lieb Liniger gas. By computing the low temperature limit of its (generalised) hydrodynamics we show how in this limit the gas is well described by a conventional viscous (Navier Stokes) hydrodynamic for density, fluid velocity and the local temperature, and the other generalised temperatures in the case of integrable gases. The dynamic viscosity is proportional to temperature and can be expressed in a universal form only in terms of the emergent Luttinger Liquid parameter K and its compressibility. We show that the heating factor is finite even in the zero temperature limit, which implies that viscous contribution remains relevant also at zero temperatures. Moreover, we find that in the semi classical limit of small couplings, kinematic viscosity diverges, reconciling with previous observations of Kardar Parisi Zhang fluctuations in mean field quantum fluids.Comment: 6 pages, 1 figures, Supplementary Materia

Lindblad-Floquet description of finite-time quantum heat engines

The operation of autonomous finite-time quantum heat engines rely on the existence of a stable limit cycle in which the dynamics becomes periodic. The two main questions that naturally arise are therefore whether such a limit cycle will eventually be reached and, once it has, what is the state of the system within the limit cycle. In this paper we show that the application of Floquet's theory to Lindblad dynamics offers clear answers to both questions. By moving to a generalized rotating frame, we show that it is possible to identify a single object, the Floquet Liouvillian, which encompasses all operating properties of the engine. First, its spectrum dictates the convergence to a limit cycle. And second, the state within the limit cycle is precisely its zero eigenstate, therefore reducing the problem to that of determining the steady-state of a time-independent master equation. To illustrate the usefulness of this theory, we apply it to a harmonic oscillator subject to a time-periodic work protocol and time-periodic dissipation, an open-system generalization of the Ermakov-Lewis theory. The use of this theory to implement a finite-time Carnot engine subject to continuous frequency modulations is also discussed

One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large NN

In one-dimensional (1D) quantum gases, the momentum distribution (MD) of the atoms is a standard experimental observable, routinely measured in various experimental setups. The MD is sensitive to correlations, and it is notoriously hard to compute theoretically for large numbers of atoms $N$, which often prevents direct comparison with experimental data. Here we report significant progress on this problem for the 1D Tonks-Girardeau (TG) gas in the asymptotic limit of large $N$, at zero temperature and driven out of equilibrium by a quench of the confining potential. We find an exact analytical formula for the one-particle density matrix $\langle \hat{\Psi}^\dagger(x) \hat{\Psi}(x') \rangle$ of the out-of-equilibrium TG gas in the $N \rightarrow \infty$ limit, valid on distances $|x-x'|$ much larger than the interparticle distance. By comparing with time-dependent Bose-Fermi mapping numerics, we demonstrate that our analytical formula can be used to compute the out-of-equilibrium MD with great accuracy for a wide range of momenta (except in the tails of the distribution at very large momenta). For a quench from a double-well potential to a single harmonic well,which mimics a `quantum Newton cradle' setup, our method predicts the periodic formation of peculiar, multiply peaked, momentum distributions.Comment: 13pages, 6 figures. v2: minor changes; v3: fixed layout issues in appendice