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 ($\alpha'$ 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 $\alpha'$ 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 $n$ instances of a stationary process from random linear projections as long as their count is slightly more than $n$ 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