arXiv subjects

G. Kunstatter

Publications and source records attributed to G. Kunstatter.

At least 19 recordsLinked to original sources

arXiv2016

Gradient Flow in the Ginzburg-Landau Model of Superconductivity

We present numerical studies of the dynamics of vortices in the Ginzburg Landau model using equations derived from the gradient flow of the free energy. These equations have previously been proposed to describe the dynamics of n-vortices away from equilibrium. We are able to model the dynamics of multiple n-vortex configurations starting far from equilibrium. We find generically that there are two time scales for equilibration: a short time scale related to the formation time for a single n-vortex, and a longer time scale that characterizes vortex-vortex interactions.

hep-th↗

arXiv2015

On the geometric measure of entanglement for pure states

The geometric measure of entanglement is the distance or angle between an entangled target state and the nearest unentangled state. Often one considers the geometric measure of entanglement for highly symmetric entangled states because it simplifies the calculations and allows for analytic solutions. Although some symmetry is required in order to deal with large numbers of qubits, we are able to loosen significantly the restrictions on the highly symmetric states considered previously, and consider several generalizations of the coefficients of both target and unentangled states. This allows us to compute the geometric entanglement measure for larger and more relevant classes of states.

quant-ph↗

arXiv2014

Critical Collapse in Einstein-Gauss-Bonnet Gravity in Five and Six Dimensions

Einstein-Gauss-Bonnet gravity (EGB) provides a natural higher dimensional and higher order curvature generalization of Einstein gravity. It contains a new, presumably microscopic, length scale that should affect short distance properties of the dynamics, such as Choptuik scaling. We present the results of a numerical analysis in generalized flat slice co-ordinates of self-gravitating massless scalar spherical collapse in five and six dimensional EGB gravity near the threshold of black hole formation. Remarkably, the behaviour is universal (i.e. independent of initial data) but qualitatively different in five and six dimensions. In five dimensions there is a minimum horizon radius, suggestive of a first order transition between black hole and dispersive initial data. In six dimensions no radius gap is evident. Instead, below the GB scale there is a change in the critical exponent and echoing period.

gr-qc↗

arXiv2012

Local Hamiltonian for Spherically Symmetric Collapse: Geometrodynamics Approach

Recently a {\it local} true (completely gauge fixed) Hamiltonian for spherically symmetric collapse was derived in terms of Ashtekar variables. We show that such a local Hamiltonian follows directly from the geometrodynamics of gravity theories that obey a Birkhoff theorem and possess a mass function that is constant on the constraint surface in vacuum. In addition to clarifying the geometrical content, our approach has the advantage that it can be directly applied to a large class of spherically symmetric and 2D gravity theories, including $p$-th order Lovelock gravity in D dimensions. The resulting expression for the true local Hamiltonian is universal and remarkably simple in form.

gr-qc↗

arXiv2011

Hamiltonian Formulation of Scalar Field Collapse in Einstein Gauss Bonnet Gravity

We compute the Hamiltonian for spherically symmetric scalar field collapse in Einstein-Gauss-Bonnet gravity in D dimensions using slicings that are regular across future horizons. We first reduce the Lagrangian to two dimensions using spherical symmetry. We then show that choosing the spatial coordinate to be a function of the areal radius leads to a relatively simple Hamiltonian constraint whose gravitational part is the gradient of the generalized mass function. Next we complete the gauge fixing such that the metric is the Einstein-Gauss-Bonnet generalization of non-static Painleve-Gullstrand coordinates. Finally, we derive the resultant reduced equations of motion for the scalar field. These equations are suitable for use in numerical simulations of spherically symmetric scalar field collapse in Gauss-Bonnet gravity and can readily be generalized to other matter fields minimally coupled to gravity.

gr-qc↗

arXiv2011

Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition

In a previous paper we examined a geometric measure of entanglement based on the minimum distance between the entangled target state of interest and the space of unnormalized product states. Here we present a detailed study of this entanglement measure for target states with a large degree of symmetry. We obtain analytic solutions for the extrema of the distance function and solve for the Hessian to show that, up to the action of trivial symmetries, the solutions correspond to local minima of the distance function. In addition, we show that the conditions that determine the extremal solutions for general target states can be obtained directly by parametrizing the product states via their Schmidt decomposition.

quant-ph↗

arXiv2010

Geometric measures of entanglement and the Schmidt decomposition

In the standard geometric approach, the entanglement of a pure state is $\sin^2θ$, where $θ$ is the angle between the entangled state and the closest separable state of products of normalised qubit states. We consider here a generalisation of this notion by considering separable states that consist of products of unnormalised states of different dimension. The distance between the target entangled state and the closest unnormalised product state can be interpreted as a measure of the entanglement of the target state. The components of the closest product state and its norm have an interpretation in terms of, respectively, the eigenvectors and eigenvalues of the reduced density matrices arising in the Schmidt decomposition of the state vector. For several cases where the target state has a large degree of symmetry, we solve the system of equations analytically, and look specifically at the limit where the number of qubits is large.

quant-ph↗

arXiv2010

Polymer quantization of the Einstein-Rosen wormhole throat

We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a radius that depends on the polymerization scale. In the polymer quantum theory, we show numerically that the area spectrum is evenly-spaced and in agreement with a Bohr-Sommerfeld semiclassical estimate, and this spectrum is not qualitatively sensitive to issues of factor ordering or boundary conditions except in the lowest few eigenvalues. In the limit of small polymerization scale we recover, within the numerical accuracy, the area spectrum obtained from a Schrodinger quantization of the wormhole throat dynamics. The prospects of recovering from the polymer throat theory a full quantum-corrected spacetime are discussed.

gr-qc↗

arXiv2009

Effective Polymer Dynamics of D-Dimensional Black Hole Interiors

We consider two different effective polymerization schemes applied to D-dimensional, spherically symmetric black hole interiors. It is shown that polymerization of the generalized area variable alone leads to a complete, regular, single-horizon spacetime in which the classical singularity is replaced by a bounce. The bounce radius is independent of rescalings of the homogeneous internal coordinate, but does depend on the arbitrary fiducial cell size. The model is therefore necessarily incomplete. It nonetheless has many interesting features: After the bounce, the interior region asymptotes to an infinitely expanding Kantowski-Sachs spacetime. If the solution is analytically continued across the horizon, the black hole exterior exhibits asymptotically vanishing quantum-corrections due to the polymerization. In all spacetime dimensions except four, the fall-off is too slow to guarantee invariance under Poincare transformations in the exterior asymptotic region. Hence the four-dimensional solution stands out as the only example which satisfies the criteria for asymptotic flatness. In this case it is possible to calculate the quantum-corrected temperature and entropy. We also show that polymerization of both phase space variables, the area and the conformal mode of the metric, generically leads to a multiple horizon solution which is reminiscent of polymerized mini-superspace models of spherically symmetric black holes in Loop Quantum Gravity.

gr-qc↗

arXiv2009

Complete, Single-Horizon Quantum Corrected Black Hole Spacetime

We show that a semi-classical polymerization of the interior of Schwarzschild black holes gives rise to a tantalizing candidate for a non-singular, single horizon black hole spacetime. The exterior has non-zero quantum stress energy but closely approximates the classical spacetime for macroscopic black holes. The interior exhibits a bounce at a microscopic scale and then expands indefinitely to a Kantowski-Sachs spacetime. Polymerization therefore removes the singularity and produces a scenario reminiscent of past proposals for universe creation via quantum effects inside a black hole.

gr-qc↗

arXiv2009

Polymer quantization, singularity resolution and the 1/r^2 potential

We present a polymer quantization of the -lambda/r^2 potential on the positive real line and compute numerically the bound state eigenenergies in terms of the dimensionless coupling constant lambda. The singularity at the origin is handled in two ways: first, by regularizing the potential and adopting either symmetric or antisymmetric boundary conditions; second, by keeping the potential unregularized but allowing the singularity to be balanced by an antisymmetric boundary condition. The results are compared to the semiclassical limit of the polymer theory and to the conventional Schrodinger quantization on L_2(R_+). The various quantization schemes are in excellent agreement for the highly excited states but differ for the low-lying states, and the polymer spectrum is bounded below even when the Schrodinger spectrum is not. We find as expected that for the antisymmetric boundary condition the regularization of the potential is redundant: the polymer quantum theory is well defined even with the unregularized potential and the regularization of the potential does not significantly affect the spectrum.

gr-qc↗

arXiv2009

Dynamical Singularity Resolution in Spherically Symmetric Black Hole Formation

We study numerically the effects of loop quantum gravity motivated corrections on massless scalar field collapse in Painlevé-Gullstrand coordinates. Near criticality, the system exhibits Choptuik scaling with the added features of a mass gap and a new scaling relationship dependant upon the quantum length scale. The quantum corrected collapse exhibits a radiation-like phase which resolves the singularity: the black hole consists of a compact region of space-time bounded by a single, smooth trapping horizon. The "evaporation" is not complete but leaves behind an outward moving remnant.

gr-qc↗

arXiv2009

2-D Midisuperspace Models for Quantum Black Holes

Dimensionally reduced spherically symmetric gravity and its generalization, generic 2-D dilaton gravity, provide ideal theoretical laboratories for the study of black hole quantum mechanics and thermodynamics. They are sufficiently simple to be tractable but contain enough structure to allow the study of many deep issues in quantum gravity, such as the endpoint of Hawking radiation and the source of black hole entropy. This article reviews recent progress in a particular geometrical approach to the study of quantum black holes in generic 2-d dilaton gravity.

gr-qc↗

arXiv2008

Spherically Symmetric Black Hole Formation in Painlevé-Gullstrand Coordinates

We perform a numerical study of black hole formation from the spherically symmetric collapse of a massless scalar field. The calculations are done in Painlevé-Gullstrand (PG) coordinates that extend across apparent horizons and allow the numerical evolution to proceed until the onset of singularity formation. We generate spacetime maps of the collapse and illustrate the evolution of apparent horizons and trapping surfaces for various initial data. We also study the critical behaviour and find the expected Choptuik scaling with universal values for the critical exponent and echoing period consistent with the accepted values of $γ=0.374$ and $Δ= 3.44$, respectively. The subcritical curvature scaling exhibits the expected oscillatory behaviour but the form of the periodic oscillations in the supercritical mass scaling relation, while universal with respect to initial PG data, is non-standard: it is non-sinusoidal with large amplitude cusps.

gr-qc↗

arXiv2007

Decoherence of a Single Qubit from Quantum Anomaly

We show via an explicit example that quantum anomalies can lead to decoherence of a single quantum qubit through phase relaxation. The anomaly causes the Hamiltonian to develop a non-self-adjoint piece due to the non-invariance of the domain of the Hamiltonian under symmetry transformation. The resulting decoherence originates completely from the dynamics of the system itself and not, as usually considered, from interactions with the environment.

quant-ph↗

arXiv2007

Geometric measures of entanglement and the Schmidt decomposition

In the standard geometric approach to a measure of entanglement of a pure state, $\sin^2θ$ is used, where $θ$ is the angle between the state to the closest separable state of products of normalized qubit states. We consider here a generalization of this notion to separable states consisting of products of unnormalized states of different dimension. In so doing, the entanglement measure $\sin^2θ$ is found to have an interpretation as the distance between the state to the closest separable state. We also find the components of the closest separable state and its norm have an interpretation in terms of, respectively, the eigenvectors and eigenvalues of the reduced density matrices arising in the Schmidt decomposition of the state vector.

quant-ph↗

arXiv2007

A Partially Gauged Fixed Hamiltonian for Scalar Field Collapse

We derive a partially gauge fixed Hamiltonian for black hole formation via real scalar field collapse. The class of models considered includes many theories of physical interest, including spherically symmetric black holes in $D$ spacetime dimensions. The boundary and gauge fixing conditions are chosen to be consistent with generalized Painleve-Gullstrand coordinates, in which the metric is regular across the black hole future horizon. The resulting Hamiltonian is remarkably simple and we argue that it provides a good starting point for studying the quantum dynamics of black hole formation.

gr-qc↗

arXiv2006

The Mystery of the Asymptotic Quasinormal Modes of Gauss-Bonnet Black Holes

We analyze the quasinormal modes of $D$-dimensional Schwarzschild black holes with the Gauss-Bonnet correction in the large damping limit and show that standard analytic techniques cannot be applied in a straightforward manner to the case of infinite damping. However, by using a combination of analytic and numeric techniques we are able to calculate the quasinormal mode frequencies in a range where the damping is large but finite. We show that for this damping region the famous $\ln(3)$ appears in the real part of the quasinormal mode frequency. In our calculations, the Gauss-Bonnet coupling, $α$, is taken to be much smaller than the parameter $μ$, which is related to the black hole mass.

gr-qc↗