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Register a new userA Spacetime Calculation of the Calabrese-Cardy Entanglement Entropy
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We calculate Sorkins spacetime entanglement entropy of a Gaussian scalar field for complementary regions in the 2d cylinder spacetime and show that it has the Calabrese-Cardy form. We find that the cut-off dependent term is universal when we use a covariant UV cut-off. In addition, we show that the relative size-dependent term exhibits complementarity. Its coefficient is however not universal and depends on the choice of pure state. It asymptotes to the universal form within a natural class of pure states.
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We consider the entanglement dynamics between two-level atoms in a rotating black hole background. In our model the two-atom system is envisaged as an open system coupled with a massless scalar field prepared in one of the physical vacuum states of interest. We employ the quantum master equation in the Born-Markov approximation in order to describe the time evolution of the atomic subsystem. We investigate two different states of motion for the atoms, namely static atoms and also stationary atoms with zero angular momentum. The purpose of this work is to expound the impact on the creation of entanglement coming from the combined action of the different physical processes underlying the Hawking effect and the Unruh-Starobinskii effect. We demonstrate that, in the scenario of rotating black holes, the degree of quantum entanglement is significantly modified due to the phenomenon of superradiance in comparison with the analogous cases in a Schwarzschild spacetime. In the perspective of a zero angular momentum observer (ZAMO), one is allowed to probe entanglement dynamics inside the ergosphere, since static observers cannot exist within such a region. On the other hand, the presence of superradiant modes could be a source for violation of complete positivity. This is verified when the quantum field is prepared in the Frolov-Thorne vacuum state. In this exceptional situation, we raise the possibility that the loss of complete positivity is due to the breakdown of the Markovian approximation, which means that any arbitrary physically admissible initial state of the two atoms would not be capable to hold, with time evolution, its interpretation as a physical state inasmuch as negative probabilities are generated by the dynamical map.
The retarded Green function for linear field perturbations of black hole spacetimes is notoriously difficult to calculate. One of the difficulties is due to a Dirac-$delta$ divergence that the Green function possesses when the two spacetime points are connected by a direct null geodesic. We present a procedure which notably aids its calculation in the case of Schwarzschild spacetime by separating this direct $delta$-divergence from the remainder of the retarded Green function. More precisely, the method consists of calculating the multipolar $ell$-modes of the direct $delta$-divergence and subtracting them from the corresponding modes of the retarded Green function. We illustrate the usefulness of the method with some specific calculations in the case of the scalar Green function and self-field for a point scalar charge in Schwarzschild spacetime.
We review aspects of the thermodynamics of black holes and in particular take into account the fact that the quantum entanglement between the degrees of freedom of a scalar field, traced inside the event horizon, can be the origin of black hole entropy. The main reason behind such a plausibility is that the well-known Bekenstein-Hawking entropy-area proportionality -- the so-called `area law of black hole physics -- holds for entanglement entropy as well, provided the scalar field is in its ground state, or in other minimum uncertainty states, such as a generic coherent state or squeezed state. However, when the field is either in an excited state or in a state which is a superposition of ground and excited states, a power-law correction to the area law is shown to exist. Such a correction term falls off with increasing area, so that eventually the area law is recovered for large enough horizon area. On ascertaining the location of the microscopic degrees of freedom that lead to the entanglement entropy of black holes, it is found that although the degrees of freedom close to the horizon contribute most to the total entropy, the contributions from those that are far from the horizon are more significant for excited/superposed states than for the ground state. Thus, the deviations from the area law for excited/superposed states may, in a way, be attributed to the far-away degrees of freedom. Finally, taking the scalar field (which is traced over) to be massive, we explore the changes on the area law due to the mass. Although most of our computations are done in flat space-time with a hypothetical spherical region, considered to be the analogue of the horizon, we show that our results hold as well in curved space-times representing static asymptotically flat spherical black holes with single horizon.
We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order Renyi entanglement entropy S_2, can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge c. We discuss the adiabatic preparation of the ground state at half-filling where we expect a CFT with c=1. This can be accomplished with a very small hoping parameter J, in contrast to existing studies with density one where a much larger J is needed. We provide two complementary methods to estimate and subtract the classical entropy generated by the experimental preparation and imaging processes. We compare numerical calculations for the classical O(2) model with a chemical potential on a 1+1 dimensional lattice, and the quantum Bose-Hubbard Hamiltonian implemented in the experiments. S_2 is very similar for the two models and follows closely the Calabrese-Cardy scaling, (c/8)ln(N_s), for N_s sites with open boundary conditions, provided that the large subleading corrections are taken into account.
We calculate Sorkins manifestly covariant entanglement entropy $mathcal{S}$ for a massive and massless minimally coupled free Gaussian scalar field for the de Sitter horizon and Schwarzschild de Sitter horizons respectively in $d > 2$. In de Sitter spacetime we restrict the Bunch-Davies vacuum in the conformal patch to the static patch to obtain a mixed state. The finiteness of the spatial $mathcal{L}^2$ norm in the static patch implies that $mathcal{S}$ is well defined for each mode. We find that $mathcal{S}$ for this mixed state is independent of the effective mass of the scalar field, and matches that of Higuchi and Yamamoto, where, a spatial density matrix was used to calculate the horizon entanglement entropy. Using a cut-off in the angular modes we show that $mathcal{S} propto A_{c}$, where $A_c$ is the area of the de Sitter cosmological horizon. Our analysis can be carried over to the black hole and cosmological horizon in Schwarzschild de Sitter spacetime, which also has finite spatial $mathcal{L}^2$ norm in the static regions. Although the explicit form of the modes is not known in this case, we use appropriate boundary conditions for a massless minimally coupled scalar field to find the mode-wise $mathcal{S}_{b,c}$, where $b,c$ denote the black hole and de Sitter cosmological horizons, respectively. As in the de Sitter calculation we see that $mathcal{S}_{b,c} propto A_{b,c}$ after taking a cut-off in the angular modes.
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