2,494 research outputs found
Thermal Quench at Finite t'Hooft Coupling
Using holography we have studied thermal electric field quench for infinite
and finite t'Hooft coupling constant. The set-up we consider here is D7-brane
embedded in ( corrected) AdS-black hole background. It is well-known
that due to a time-dependent electric field on the probe brane, a
time-dependent current will be produced and it will finally relax to its
equilibrium value. We have studied the effect of different parameters of the
system on equilibration time. As the most important results, we have observed a
universal behaviour in the rescaled equilibration time in the very fast quench
regime for different values of the temperature and correction
parameter. It seems that in the slow quench regime the system behaves
adiabatically. We have also observed that the equilibration time decreases in
finite t'Hooft coupling limit.Comment: 6 pages, 9 figure
Probe Branes Thermalization in External Electric and Magnetic Fields
We study thermalization on rotating probe branes in AdS_5 x S^5 background in
the presence of constant external electric and magnetic fields. In the AdS/CFT
framework this corresponds to thermalization in the flavour sector in field
theory. The horizon appears on the worldvolume of the probe brane due to its
rotation in one of the sphere directions. For both electric and magnetic fields
the behaviour of the temperature is independent of the probe brane dimension.
We also study the open string metric and the fluctuations of the probe brane in
such a set-up. We show that the temperatures obtained from open string metric
and observed by the fluctuations are larger than the one calculated from the
induced metric.Comment: 27 pages, 7 figure
Far-from-equilibrium initial conditions probed by a nonlocal observable
Using the gauge/gravity duality, we investigate the evolution of an
out-of-equilibrium strongly-coupled plasma from the viewpoint of the two-point
function of scalar gauge-invariant operators with large conformal dimension.
This system is out of equilibrium due to the presence of anisotropy and/or a
massive scalar field. Considering various functions for the initial anisotropy
and scalar field, we conclude that the effect of the anisotropy on the
evolution of the two-point function is considerably more than the effect of the
scalar field. We also show that the ordering of the equilibration time of the
one-point function for the non-probe scalar field and the correlation function
between two points with a fixed separation can be reversed by changing the
initial configuration of the plasma, when the system is out of the equilibrium
due to the presence of at least two different sources like our problem. In
addition, we find the equilibration time of the two-point function to be
linearly increasing with respect to the separation of the two points with a
fixed slope, regardless of the initial configuration that we start with.
Finally we observe that, for larger separations the geodesic connecting two
points on the boundary crosses the event horizon after it has reached its final
equilibrium value, meaning that the two-point function can probe behind the
event horizon
Compression-Based Compressed Sensing
Modern compression algorithms exploit complex structures that are present in
signals to describe them very efficiently. On the other hand, the field of
compressed sensing is built upon the observation that "structured" signals can
be recovered from their under-determined set of linear projections. Currently,
there is a large gap between the complexity of the structures studied in the
area of compressed sensing and those employed by the state-of-the-art
compression codes. Recent results in the literature on deterministic signals
aim at bridging this gap through devising compressed sensing decoders that
employ compression codes. This paper focuses on structured stochastic processes
and studies the application of rate-distortion codes to compressed sensing of
such signals. The performance of the formerly-proposed compressible signal
pursuit (CSP) algorithm is studied in this stochastic setting. It is proved
that in the very low distortion regime, as the blocklength grows to infinity,
the CSP algorithm reliably and robustly recovers instances of a stationary
process from random linear projections as long as their count is slightly more
than times the rate-distortion dimension (RDD) of the source. It is also
shown that under some regularity conditions, the RDD of a stationary process is
equal to its information dimension (ID). This connection establishes the
optimality of the CSP algorithm at least for memoryless stationary sources, for
which the fundamental limits are known. Finally, it is shown that the CSP
algorithm combined by a family of universal variable-length fixed-distortion
compression codes yields a family of universal compressed sensing recovery
algorithms
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