34 research outputs found
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 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 with saturated density . The
gas is suddenly released into a region of size 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 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
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 , 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 , 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 of the out-of-equilibrium TG gas in the limit,
valid on distances 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