1,122 research outputs found
Memory-preserving equilibration after a quantum quench in a 1d critical model
One of the fundamental principles of statistical physics is that only partial
information about a system's state is required for its macroscopic description.
This is not only true for thermal ensembles, but also for the unconventional
ensemble, known as Generalized Gibbs Ensemble (GGE), that is expected to
describe the relaxation of integrable systems after a quantum quench. By
analytically studying the quench dynamics in a prototypical one-dimensional
critical model, the massless free bosonic field theory, we find evidence of a
novel type of equilibration characterized by the preservation of an enormous
amount of memory of the initial state that is accessible by local measurements.
In particular, we show that the equilibration retains memory of non-Gaussian
initial correlations, in contrast to the case of massive free evolution which
erases all such memory. The GGE in its standard form, being a Gaussian
ensemble, fails to predict correctly the equilibrium values of local
observables, unless the initial state is Gaussian itself. Our findings show
that the equilibration of a broad class of quenches whose evolution is
described by Luttinger liquid theory with an initial state that is non-Gaussian
in terms of the bosonic field, is not correctly captured by the corresponding
bosonic GGE, raising doubts about the validity of the latter in general
one-dimensional gapless integrable systems such as the Lieb-Liniger model. We
also propose that the same experiment by which the GGE was recently observed
[Langen et al., Science 348 (2015) 207-211] can also be used to observe its
failure, simply by starting from a non-Gaussian initial state.Comment: 8 pages, final version as accepted for publicatio
Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
We study the quench dynamics in continuous relativistic quantum field theory,
more specifically the locality properties of the large time stationary state.
After a quantum quench in a one-dimensional integrable model, the expectation
values of local observables are expected to relax to a Generalized Gibbs
Ensemble (GGE), constructed out of the conserved charges of the model.
Quenching to a free bosonic theory, it has been shown that the system indeed
relaxes to a GGE described by the momentum mode occupation numbers. We first
address the question whether the latter can be written directly in terms of
local charges and we find that, in contrast to the lattice case, this is not
possible in continuous field theories. We then investigate the less stringent
requirement of the existence of a sequence of truncated local GGEs that
converges to the correct steady state, in the sense of the expectation values
of the local observables. While we show that such a sequence indeed exists, in
order to unequivocally determine the so-defined GGE, we find that information
about the expectation value of the recently discovered quasi-local charges is
in the end necessary, the latter being the suitable generalization of the local
charges while passing from the lattice to the continuum. Lastly, we study the
locality properties of the GGE and show that the latter is completely
determined by the knowledge of the expectation value of a countable set of
suitably defined quasi-local charges
Quantum quench in interacting field theory: a self-consistent approximation
We study a composite quantum quench of the energy gap and the interactions in
the interacting \phi^4 model using a self-consistent approximation. Firstly we
review the results for free theories where a quantum quench of the energy gap
or mass leads for long times to stationary behaviour with thermal
characteristics. An exception to this rule is the 2d case with zero mass after
the quench. In the composite quench however we find that the effect of the
interactions in our approximation is simply to effectively change the value of
the mass. This means on the one hand that the interacting model also exhibits
the same stationary behaviour and on the other hand that this is now true even
for the massless 2d case.Comment: 20 pages, 15 figures / new citations added, minor changes, typos
corrected
Initial states in integrable quantum field theory quenches from an integral equation hierarchy
We consider the problem of determining the initial state of integrable
quantum field theory quenches in terms of the post-quench eigenstates. The
corresponding overlaps are a fundamental input to most exact methods to treat
integrable quantum quenches. We construct and examine an infinite integral
equation hierarchy based on the form factor bootstrap, proposed earlier as a
set of conditions deter- mining the overlaps. Using quenches of the mass and
interaction in Sinh-Gordon theory as a concrete example, we present theoretical
arguments that the state has the squeezed coherent form expected for integrable
quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover
we also develop an iterative method to solve numerically the lowest equation of
the hierarchy. The iterative solution along with extensive numerical checks
performed using the next equation of the hierarchy provide a strong numerical
evidence that the proposed Ansatz gives a very good approximation for the
solution.Comment: 36 pages, pdflatex file, 11 pdf figures. v2: revised version,
accepted for publicatio
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