Aspects of Holographic Entanglement at Finite Temperature and Chemical Potential

We investigate the behavior of entanglement entropy at finite temperature and chemical potential for strongly coupled large-N gauge theories in $d$-dimensions ($d\ge 3$) that are dual to Anti-de Sitter-Reissner-Nordstrom geometries in $(d+1)-$dimensions, in the context of gauge-gravity duality. We develop systematic expansions based on the Ryu-Takayanagi prescription that enable us to derive analytic expressions for entanglement entropy and mutual information in different regimes of interest. Consequently, we identify the specific regions of the bulk geometry that contribute most significantly to the entanglement entropy of the boundary theory at different limits. We define a scale, dubbed as the effective temperature, which determines the behavior of entanglement in different regimes. At high effective temperature, entanglement entropy is dominated by the thermodynamic entropy, however, mutual information subtracts out this contribution and measures the actual quantum entanglement. Finally, we study the entanglement/disentanglement transition of mutual information in the presence of chemical potential which shows that the quantum entanglement between two sub-regions decreases with the increase of chemical potential.Comment: 38 pages, multiple figure

Phase diagram of a bidispersed hard rod lattice gas in two dimensions

We obtain, using extensive Monte Carlo simulations, virial expansion and a high-density perturbation expansion about the fully packed monodispersed phase, the phase diagram of a system of bidispersed hard rods on a square lattice. We show numerically that when the length of the longer rods is $7$, two continuous transitions may exist as the density of the longer rods in increased, keeping the density of shorter rods fixed: first from a low-density isotropic phase to a nematic phase, and second from the nematic to a high-density isotropic phase. The difference between the critical densities of the two transitions decreases to zero at a critical density of the shorter rods such that the fully packed phase is disordered for any composition. When both the rod lengths are larger than $6$, we observe the existence of two transitions along the fully packed line as the composition is varied. Low-density virial expansion, truncated at second virial coefficient, reproduces features of the first transition. By developing a high-density perturbation expansion, we show that when one of the rods is long enough, there will be at least two isotropic-nematic transitions along the fully packed line as the composition is varied.Comment: 7 pages, 4 figure

Entanglement and out-of-equilibrium dynamics in holographic models of de Sitter QFTs

In this paper we study various aspects of entanglement entropy in strongly-coupled de Sitter quantum field theories in various dimensions. We find gravity solutions that are dual to field theories in a fixed de Sitter background, both in equilibrium and out-of-equilibrium configurations. The latter corresponds to the Vaidya generalization of the AdS black hole solutions with hyperbolic topology. We compute analytically the entanglement entropy of spherical regions and show that there is a transition when the sphere is as big as the horizon. We also explore thermalization in time-dependent situations in which the system evolves from a non-equilibrium state to the Bunch-Davies state. We find that the saturation time is equal to the light-crossing time of the sphere. This behavior is faster than random walk and suggests the existence of free light-like degrees of freedom.Comment: 39 pages, 11 figures; minor changes, conclusions unchange

Strong Subadditivity, Null Energy Condition and Charged Black Holes

Using the Hubeny-Rangamani-Takayanagi (HRT) conjectured formula for entanglement entropy in the context of the AdS/CFT correspondence with time-dependent backgrounds, we investigate the relation between the bulk null energy condition (NEC) of the stress-energy tensor with the strong sub-additivity (SSA) property of entanglement entropy in the boundary theory. In a background that interpolates between an AdS to an AdS-Reissner-Nordstrom-type geometry, we find that generically there always exists a critical surface beyond which the violation of NEC would naively occur. However, the extremal area surfaces that determine the entanglement entropy for the boundary theory, can penetrate into this forbidden region only for certain choices for the mass and the charge functions in the background. This penetration is then perceived as the violation of SSA in the boundary theory. We also find that this happens only when the critical surface lies above the apparent horizon, but not otherwise. We conjecture that SSA, which is thus non-trivially related to NEC, also characterizes the entire time-evolution process along which the dual field theory may thermalize.Comment: 27 pages, v3 matches the published versio

Weak Field Collapse in AdS: Introducing a Charge Density

We study the effect of a non-vanishing chemical potential on the thermalization time of a strongly coupled large $N_c$ gauge theory in $(2+1)$-dimensions, using a specific bottom-up gravity model in asymptotically AdS space. We first construct a perturbative solution to the gravity-equations, which dynamically interpolates between two AdS black hole backgrounds with different temperatures and chemical potentials, in a perturbative expansion of a bulk neutral scalar field. In the dual field theory, this corresponds to a quench dynamics by a marginal operator, where the corresponding coupling serves as the small parameter in which the perturbation is carried out. The evolution of non-local observables, such as the entanglement entropy, suggests that thermalization time decreases with increasing chemical potential. We also comment on the validity of our perturbative analysis.Comment: 1+48 pages, multiple figures, published in JHE

Linear response formula for finite frequency thermal conductance of open systems

An exact linear response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present numerical results on the frequency dependence of the response function for three different one-dimensional models of coupled oscillators connected to Langevin baths with oscillating temperatures. For momentum conserving systems, a low frequency peak is seen that, is higher than the zero frequency response for large systems. For momentum non-conserving systems, there is no low frequency peak. The momentum non-conserving system is expected to satisfy Fourier's law, however, at the single bond level, we do not see any clear agreement with the predictions of the diffusion equation even at low frequencies. We also derive an exact analytical expression for the response of a chain of harmonic oscillators to a (not necessarily small) temperature difference; the agreement with the linear response simulation results for the same system is excellent.Comment: 8 pages, 7 figure

OH(1720 MHz) Masers As Signposts of Molecular Shocks

We present observations of molecular gas made with the 15-m James Clark Maxwell Telescope toward the sites of OH(1720 MHz) masers in three supernova remnants: W28, W44 and 3C391. Maps made in the 12CO J=3-2 line reveal that the OH masers are preferentially located along the edges of thin filaments or clumps of molecular gas. There is a strong correlation between the morphology of the molecular gas and the relativistic gas traced by synchrotron emission at centimeter wavelengths. Broad CO line widths (dV=30-50 km/s) are seen along these gaseous ridges, while narrow lines are seen off the ridges. The ratio of H2CO line strengths is used to determine temperatures in the broad-line gas of 80 K, and the 13CO J=3-2 column density suggests densities of 10^4-10^5 cm{-3}. These observations support the hypothesis that the OH(1720 MHz) masers originate in post-shock gas, heated by the passage of a supernova remnant shock through dense molecular gas. From the observational constraints on the density, velocity and magnetic field we examine the physical properties of the shock and discuss the shock-production of OH. These OH(1720 MHz) masers are useful ``signposts'', which point to the most promising locations to study supernova remnant/molecular cloud interactions.Comment: ApJ (in press

Geodesic Distance Histogram Feature for Video Segmentation

This paper proposes a geodesic-distance-based feature that encodes global information for improved video segmentation algorithms. The feature is a joint histogram of intensity and geodesic distances, where the geodesic distances are computed as the shortest paths between superpixels via their boundaries. We also incorporate adaptive voting weights and spatial pyramid configurations to include spatial information into the geodesic histogram feature and show that this further improves results. The feature is generic and can be used as part of various algorithms. In experiments, we test the geodesic histogram feature by incorporating it into two existing video segmentation frameworks. This leads to significantly better performance in 3D video segmentation benchmarks on two datasets