In this article we show that the asymptotic iteration method (AIM) allows one to numerically find the quasinormal modes of Schwarzschild and Schwarzschild de Sitter (SdS) black holes. An added benefit of the method is that it can also be used to calculate the Schwarzschild anti-de Sitter (SAdS) quasinormal modes for the case of spin zero perturbations. We also discuss an improved version of the AIM, more suitable for numerical implementation. ¶ Main address from 1st of June. 1 The phrase "continued fraction" used for WKB solutions should not be confused with the type of continued fractions developed from Frobenius series for QNMs by Leaver [2]. In the rest of the paper "continued fraction" will mean those generated from Frobenius series.

We discuss an approach to obtaining black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second order ordinary differential equations.We introduce the standard version of this method and present an improvement more suitable for numerical implementation. We demonstrate that the AIM can be used to find radial QNMs for Schwarzschild, Reissner-Nordström (RN) and Kerr black holes in a unified way. An advantage of the AIM over the standard continued fraction method (CFM) is that for differential equations with more than three regular singular points Gaussian eliminations are not required. However, the convergence of the AIM depends on the location of the radial or angular position, choosing the best such position in general remains an open problem. This review presents for the first time the spin 0, 1/2 & 2 QNMs of a Kerr black hole and the gravitational and electromagnetic QNMs of the RN black hole calculated via the AIM, and confirms results previously obtained using the CFM.We also presents some new results comparing the AIM to the WKB method. Finally we emphasize that the AIM is well suited to higher dimensional generalizations and we give an example of doubly rotating black holes.

In this paper we use the conformal properties of the spinor field to show how we can obtain the fermion quasi-normal modes for a higher dimensional Schwarzschild black hole. These modes are of interest in so called split fermion models, where quarks and leptons are required to exist on different branes in order to keep the proton stable. As has been previously shown, for brane localized fields, the larger the number of dimensions the faster the black hole damping rate. Moreover, we also present the analytic forms of the quasi-normal frequencies in both the large angular momentum and the large mode number limits.

We propose a projective operator formalism that is well-suited to study the correlations of quantum fields in non-inertial frames. We generalise a Glauber model of detection of a single localised field mode that is capable of making measurements in an arbitrary reference frame. We show that the model correctly reproduces the Unruh temperature formula of a single accelerated detector, and use it to extract vacuum entanglement by a pair of counter-accelerating detectors. This latter example is a proof of principle that this approach will be appropriate to further studies on the nature of entanglement in non-inertial frames and, in general, to model experimentally feasible scenarios in quantum field theory in non-inertial frames. Finally, as further confirmation of the validity of our approach, we introduce an explicit perturbative matter-radiation interaction model which reproduces both the generalised Glauber model and the projective measurement results in the weak coupling regime. arXiv:1203.0655v2 [quant-ph] 1 Dec 2012

The Unruh effect refers to the thermal fluctuations a detector experiences while undergoing linear motion with uniform acceleration in a Minkowski vacuum. This thermality can be demonstrated by tracing the vacuum state of the field over the modes beyond the accelerated detector's event horizon. However, the event horizon is well-defined only if the detector moves with eternal uniform linear acceleration. This idealized condition cannot be fulfilled in realistic situations when the motion unavoidably involves periods of non-uniform acceleration. Many experimental proposals to test the Unruh effect are of this nature. Often circular or oscillatory motion, which lacks an obvious geometric description, is considered in such proposals. The proper perspective for theoretically going beyond, or experimentally testing, the Unruh-Hawking effect in these more general conditions has to be offered by concepts and techniques in non-equilibrium quantum field theory. In this paper we provide a detailed analysis of how an Unruh-DeWitt detector undergoing oscillatory motion responds to the fluctuations of a quantum field. Numerical results for the late-time temperatures of the oscillating detector are presented. We comment on the digressions of these results from what one would obtain from a naive application of Unruh's result.Keywords: quantum dissipative system, boundary quantum field theory, black holes.

We investigate the amount of entanglement and quantum discord extractable from a two mode squeezed state as considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated). We find that using localized modes produces qualitatively different correlation properties for large accelerations than do Unruh modes. Specifically, the entanglement undergoes a sudden death as a function of acceleration and the discord asymptotes to zero in the limit of infinite acceleration. We conclude that the previous Unruh mode analyses do not determine the acceleration dependent entanglement and discord degradation of a given quantum state.

Using an open quantum system we calculate the time dependence of the concurrence between two maximally entangled electron spins with one accelerated uniformly in the presence of constant electric and magnetic fields and the other at rest and isolated from fields. We find at high Rindler temperature the proper time for the entanglement to be extinguished is proportional to the inverse of the acceleration cubed.

We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behavior of this process is similar to the analogous process on the square lattice. However, while the square lattice process maps to the collapse transition of the canonical interacting self-avoiding trail (ISAT) model on that lattice, the process on the triangular lattice model does not map to the canonical equilibrium model. On the other hand, we show that the collapse transition of the canonical ISAT model on the triangular lattice behaves in a way reminiscent of the θ point of the interacting self-avoiding walk (ISAW) model, which is the standard model of polymer collapse. This implies an unusual lattice dependency of the ISAT collapse transition in two dimensions. By studying an extended ISAT model, we demonstrate that the growth process maps to a multicritical point in a larger parameter space. In this extended parameter space the collapse phase transition may be either θ-point-like (second order) or first order, and these two are separated by a multicritical point. It is this multicritical point to which the growth process maps. Furthermore, we provide evidence that in addition to the high-temperature gaslike swollen polymer phase (coil) and the low-temperature liquid-drop-like collapse phase (globule) there is also a maximally dense crystal-like phase (crystal) at low temperatures dependent on the parameter values. The multicritical point is the meeting point of these three phases. Our hypothesized phase diagram resolves the mystery of the seemingly differing behaviors of the ISAW and ISAT models in two dimensions as well as the behavior of the trail growth process.