24,236 research outputs found
Perturbative large deviation analysis of non-equilibrium dynamics
Macroscopic fluctuation theory has shown that a wide class of non-equilibrium
stochastic dynamical systems obey a large deviation principle, but except for a
few one-dimensional examples these large deviation principles are in general
not known in closed form. We consider the problem of constructing successive
approximations to an (unknown) large deviation functional and show that the
non-equilibrium probability distribution the takes a Gibbs-Boltzmann form with
a set of auxiliary (non-physical) energy functions. The expectation values of
these auxiliary energy functions and their conjugate quantities satisfy a
closed system of equations which can imply a considerable reduction of
dimensionality of the dynamics. We show that the accuracy of the approximations
can be tested self-consistently without solving the full non- equilibrium
equations. We test the general procedure on the simple model problem of a
relaxing 1D Ising chain.Comment: 21 pages, 10 figure
Holographic Evolution of Entanglement Entropy
We study the evolution of entanglement entropy in a 2-dimensional
equilibration process that has a holographic description in terms of a Vaidya
geometry. It models a unitary evolution in which the field theory starts in a
pure state, its vacuum, and undergoes a perturbation that brings it far from
equilibrium. The entanglement entropy in this set up provides a measurement of
the quantum entanglement in the system. Using holographic techniques we recover
the same result obtained before from the study of processes triggered by a
sudden change in a parameter of the hamiltonian, known as quantum quenches.
Namely, entanglement in 2-dimensional conformal field theories propagates with
velocity v^2=1. Both in quantum quenches and in the Vaidya model equilibration
is only achieved at the local level. Remarkably, the holographic derivation of
this last fact requires information from behind the apparent horizon generated
in the process of gravitational collapse described by the Vaidya geometry. In
the early stages of the evolution the apparent horizon seems however to play no
relevant role with regard to the entanglement entropy. We speculate on the
possibility of deriving a thermalization time for occupation numbers from our
analysis.Comment: 26 pages, 10 figure
Fluctuations of an evaporating black hole from back reaction of its Hawking radiation: Questioning a premise in earlier work
This paper delineates the first steps in a systematic quantitative study of
the spacetime fluctuations induced by quantum fields in an evaporating black
hole. We explain how the stochastic gravity formalism can be a useful tool for
that purpose within a low-energy effective field theory approach to quantum
gravity. As an explicit example we apply it to the study of the
spherically-symmetric sector of metric perturbations around an evaporating
black hole background geometry. For macroscopic black holes we find that those
fluctuations grow and eventually become important when considering sufficiently
long periods of time (of the order of the evaporation time), but well before
the Planckian regime is reached. In addition, the assumption of a simple
correlation between the fluctuations of the energy flux crossing the horizon
and far from it, which was made in earlier work on spherically-symmetric
induced fluctuations, is carefully analyzed and found to be invalid. Our
analysis suggests the existence of an infinite amplitude for the fluctuations
of the horizon as a three-dimensional hypersurface. We emphasize the need for
understanding and designing operational ways of probing quantum metric
fluctuations near the horizon and extracting physically meaningful information.Comment: 10 pages, REVTeX; minor changes, a few references added and a brief
discussion of their relevance included. To appear in the proceedings of the
10th Peyresq meeting. Dedicated to Rafael Sorkin on the occasion of his 60th
birthda
Holographic Thermalization
Using the AdS/CFT correspondence, we probe the scale-dependence of
thermalization in strongly coupled field theories following a quench, via
calculations of two-point functions, Wilson loops and entanglement entropy in
d=2,3,4. In the saddlepoint approximation these probes are computed in AdS
space in terms of invariant geometric objects - geodesics, minimal surfaces and
minimal volumes. Our calculations for two-dimensional field theories are
analytical. In our strongly coupled setting, all probes in all dimensions share
certain universal features in their thermalization: (1) a slight delay in the
onset of thermalization, (2) an apparent non-analyticity at the endpoint of
thermalization, (3) top-down thermalization where the UV thermalizes first. For
homogeneous initial conditions the entanglement entropy thermalizes slowest,
and sets a timescale for equilibration that saturates a causality bound over
the range of scales studied. The growth rate of entanglement entropy density is
nearly volume-independent for small volumes, but slows for larger volumes.Comment: 39 pages, 24 figure
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