arXiv subjects

Ingemar Bengtsson

Publications and source records attributed to Ingemar Bengtsson.

At least 91 records · Page 5Linked to original sources

arXiv2004

Birkhoff's polytope and unistochastic matrices, N=3 and N=4

The set of bistochastic or doubly stochastic N by N matrices form a convex set called Birkhoff's polytope, that we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff's polytope. For N=3 we present fairly complete results. For N=4 partial results are obtained. An interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der Waerden matrix for N=3, while this is not the case for N=4.

math.CO↗

arXiv2004

On duality between quantum maps and quantum states

We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations, determined by unitary matrices of extended dimensionality, is defined and analyzed. Using the concept of the dynamical matrix and the Jamiolkowski isomorphism we explore the relation between the set of quantum operations (dynamics) and the set of density matrices acting on an extended Hilbert space (kinematics). An analogous relation is established between the classical maps and an extended space of the discrete probability distributions.

quant-ph↗

arXiv2003

Geometry of black hole thermodynamics

The Hessian of the entropy function can be thought of as a metric tensor on the state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study this geometry for some families of black holes. It is flat for the BTZ and Reissner-Nordstrom black holes, while curvature singularities occur for the Reissner-Nordstrom-anti-de Sitter and Kerr black holes.

gr-qc↗

arXiv2003

How to mix a density matrix

A given density matrix may be represented in many ways as a mixture of pure states. We show how any density matrix may be realized as a uniform ensemble. It has been conjectured that one may realize all probability distributions that are majorized by the vector of eigenvalues of the density matrix. We show that if the states in the ensemble are assumed to be distinct then it is not true, but a marginally weaker statement may still be true.

quant-ph↗

arXiv2001

Relativity of pure states entanglement

Entanglement of any pure state of an N times N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized entropies of the vector of Schmidt coefficients. For N >= 3 they generate different ordering in the set of pure states and for some states their ordering depends on the measure of entanglement used. This odd-looking property is acceptable, since these incomparable states cannot be transformed to each other with unit efficiency by any local operation. In analogy to special relativity the set of pure states equivalent under local unitaries has a causal structure so that at each point the set splits into three parts: the 'Future', the 'Past' and the set of noncomparable states.

quant-ph↗

arXiv2000

2+1 gravity, chaos and time machines

2+1 gravity for spacetimes with topology RxT^2 has been much studied. We add a description of how to extend these spacetimes across a Cauchy horizon into a region where the torus becomes Lorentzian. The result is a one parameter family of tori given by a geodesic in the "Teichmueller space" of Lorentzian tori. We describe this in detail. We also point out that if the modular group is regarded as part of the gauge group then these spacetimes offer a nice toy model for the dynamics of Bianchi IX models; in the region where the tori are spacelike the dynamics is described exactly by a hyperbolic billiard. On the other hand the modular group acts ergodically on the Teichmueller space of Lorentzian tori.

gr-qc↗

arXiv2000

A note on topological brane theories

We consider the theory of closed $p$-branes propagating on $(p+1)$-dimensional space-time manifolds. This theory has no local degrees of freedom. Here we study its canonical and BRST structures of the theory. In the case of locally flat backgrounds one can show that the $p$-brane theory is related to another known topological field theory. In the general situation some equivalent actions can also be written for the topological $p$-brane theory.

hep-th↗

arXiv1999

De Sitter Space and Spatial Topology

Morrow-Jones and Witt have shown that generic spatial topologies admit initial data that evolve to locally de Sitter spacetimes under Einstein's equations. We simplify their arguments, make them a little more general, and solve for the global time evolution of the wormhole initial data considered by them. Finally we give explicit examples of locally de Sitter domains of development whose universal covers cannot be embedded in de Sitter space.

gr-qc↗

arXiv1999

A Spinning Anti-de Sitter Wormhole

We construct a 2+1 dimensional spacetime of constant curvature whose spatial topology is that of a torus with one asymptotic region attached. It is also a black hole whose event horizon spins with respect to infinity. An observer entering the hole necessarily ends up at a "singularity"; there are no inner horizons. In the construction we take the quotient of 2+1 dimensional anti-de Sitter space by a discrete group Gamma. A key part of the analysis proceeds by studying the action of Gamma on the boundary of the spacetime.

gr-qc↗

arXiv1999

Degenerate Metric Phase Boundaries

The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such "phase boundaries" in which the metric is degenerate on one side of a null hypersurface and non-degenerate on the other side. These include portions of flat space, Schwarzschild, and plane wave solutions joined to degenerate regions. In the last case, the wave collides with a planar phase boundary and continues on with the same curvature but degenerate triad, while the phase boundary continues in the opposite direction. We conjecture that degenerate phase boundaries are always null.

gr-qc↗

arXiv1997

Black Holes and Wormholes in 2+1 Dimensions

A large variety of spacetimes---including the BTZ black holes---can be obtained by identifying points in 2+1 dimensional anti-de Sitter space by means of a discrete group of isometries. We consider all such spacetimes that can be obtained under a restriction to time symmetric initial data and one asymptotic region only. The resulting spacetimes are non-eternal black holes with collapsing wormhole topologies. Our approach is geometrical, and we discuss in detail: The allowed topologies, the shape of the event horizons, topological censorship and trapped curves.

gr-qc↗

arXiv1996

Manifest Duality in Born-Infeld Theory

Born-Infeld theory is formulated using an infinite set of gauge fields, along the lines of McClain, Wu and Yu. In this formulation electromagnetic duality is generated by a fully local functional. The resulting consistency problems are analyzed and the formulation is shown to be consistent.

hep-th↗

arXiv1996

On Chiral p-Forms

Some aspects of chiral p-forms, in particular the obstruction that makes it hard to define covariant Green functions, are discussed. It is shown that a proposed resolution involving an infinite set of gauge fields can be made mathematically rigourous in the classical case. We also give a brief demonstration of species doubling for chiral bosons.

hep-th↗

arXiv1996

Making Anti-de Sitter Black Holes

It is known from the work of Banados et al. that a space-time with event horizons (much like the Schwarzschild black hole) can be obtained from 2+1 dimensional anti-de Sitter space through a suitable identification of points. We point out that this can be done in 3+1 dimensions as well. In this way we obtain black holes with event horizons that are tori or Riemann surfaces of genus higher than one. They can have either one or two asymptotic regions. Locally, the space-time is isometric to anti-de Sitter space.

gr-qc↗

arXiv1995

Neighbours of Einstein's Equations: Connections and Curvatures

Once the action for Einstein's equations is rewritten as a functional of an SO(3,C) connection and a conformal factor of the metric, it admits a family of ``neighbours'' having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in general very complicated. The Einstein case is distinguished by the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the general case the theory is bimetric on the fibers.

gr-qc↗

arXiv1995

Form Geometry and the 'tHooft-Plebanski Action

Riemannian geometry in four dimensions, including Einstein's equations, can be described by means of a connection that annihilates a triad of two-forms (rather than a tetrad of vector fields). Our treatment of the conformal factor of the metric differs from the original presentation of this result, due to 'tHooft. In the action the conformal factor now appears as a field to be varied.

gr-qc↗

arXiv1994

Note on Massive Spin 2 in Curved Space

We give a Hamiltonian formulation of massive spin 2 theory in arbitrary Einstein space-times. We pay particular attention to Higuchi's forbidden mass range in deSitter space.

gr-qc↗

arXiv1993

Form Connections

Riemannian geometry in four dimensions naturally leads to an SL(3) connection that annihilates a basis for self-dual two-forms. Einstein's equations may be written in terms of an SO(3) connection, with SO(3) chosen as an appropriate subgroup of SL(3). We show how a set of "neighbours" of Einstein's equations arises because the subgroup may be chosen in different ways. An explicit example of a non-Einstein metric obtained in this way is given. Some remarks on three dimensional space-times are made.

gr-qc↗