120058153
Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate killing horizon
Abstract This paper is concerned with the study of quasifree states of a linear, scalar quantum field in globally hyperbolic spacetimes possessing a one-parameter group of isometries with a bifurcate Killing horizon. Some results on the uniqueness and thermal properties of such states are well known in the special cases of Minkowski, Schwarzschild, and deSitter spacetimes, and our main aim is to present new stronger results and to generalize them to this wide class of spacetimes. As a preliminary to proving our theorems, we develop some aspects of the theory of globally of hyperbolic spacetimes with a bifurcate Killing horizon, we give some new results on the structure of Bose quasifree states of linear fields (the class which includes all the usual “Fock vacua”), and we clarify and further develop the notion of a “Hadamard state”. We then consider the quasifre e states on these spacetimes which have vanishing one-point function, are invariant under the one-parameter isometry group, and are nonsingular in a neighborhood of the horizon in the sense that their two-point function is of the Hadamard form there. We prove that, on a large subalgebra of observables (which are determined by observables localized in compact regions of the horizon) such states are unique and pure. Furthermore, if the spacetime admits a certain discrete “wedge reflection” isometry (as holds automatically in the analytic case) we prove that this state - if it exists - must be a KMS state at the Hawking temperature T = κ /2 π when restricted to those observables in our subalgebra which are localized in one of the (“right” or “left”) wedges of the spacetime where the Killing orbits are timelike near the horizon. Here, κ denotes the surface g ravity of the horizon. Under the further assumption that the nonsingularity of the state holds globally and that there are no “zero modes” in the one-partic le Hilbert space belonging to the state, we extend the uniqueness result to all observables localized in the full “domain of determinacy” of the hori zon. However, existence of states satisfying the hypotheses of our theorems does not hold in general and, indeed, we prove the nonexistence of any stationary (not necessarily quasifree) Hadamard state on the Schwarzschild-deSitter and Kerr spacetimes. We remark that nowhere in the analysis do we need to assume any form of Einstein's equations.
124668258
Purification of Kms States
On presente des resultats fondamentaux sur les etats KMS a partir d'une approche nouvelle suggeree a la fois par le probleme de purification et aussi par la situation de Bisognano-Wichmaun
122720815
THE PRINCIPLE OF LOCALITY AND QUANTUM FIELD THEORY ON (NON GLOBALLY HYPERBOLIC) CURVED SPACETIMES
In the context of a linear model (the covariant Klein Gordon equation) we review the mathematical and conceptual framework of quantum field theory on globally hyperbolic spacetimes, and address the question of what it might mean to quantize a field on a non globally hyperbolic spacetime. Our discussion centres on the notion of F-locality which we introduce and which asserts there is a net of local algebras such that every neighbourhood of every point contains a globally hyperbolic subneighbourhood of that point for which the field algebra coincides with the algebra one would obtain were one to regard the subneighbourhood as a spacetime in its own right and quantize — with some choice of time-orientation — according to the standard rules for quantum field theory on globally hyperbolic spacetimes. We show that F-locality is a property of the standard field algebra construction for globally hyperbolic spacetimes, and argue that it (or something similar) should be imposed as a condition on any field algebra construction for non globally hyperbolic spacetimes. We call a spacetime for which there exists a field algebra satisfying F-locality F-quantum compatible and argue that a spacetime which did not satisfy something similar to this condition could not arise as an approximate classical description of a state of quantum gravity and would hence be ruled out physically. We show that all F-quantum compatible spacetimes are time orientable. We also raise the issue of whether chronology violating spacetimes can be F-quantum compatible, giving a special model — a massless field theory on the “four dimensional spacelike cylinder” — which is F-quantum compatible, and a (two dimensional) model — a massless field theory on Misner space — which is not. We discuss the possible relevance of this latter result to Hawking’s recent Chronology Protection Conjecture.
5060903
Monotonicity with volume of entropy and of mean entropy for translationally invariant systems as consequences of strong subadditivity
We consider some questions concerning the monotonicity properties of entropy and of mean entropy for translationally invariant states on translationally invariant systems (classical lattice, quantum lattice and quantum continuous). By taking the property of strong subadditivity, which for quantum systems was proven rather late in the historical development, as one of four primary axioms (the other three being simply positivity, subadditivity and translational invariance), we are able to obtain results, some new, some proved in a new way, which appear to complement in an interesting way results proved around 30 years ago on limiting mean entropy and related questions. In particular, we prove that as the sizes of boxes in Z ν or R ν increase in the sense of set inclusion, (1) their mean entropy decreases monotonically and (2) their entropy increases monotonically. We include a proof of (2) based on the notion of mpoint correlation entropies, which we introduce and which generalize the notion of index of correlation (see e.g. Horodecki R 1994 Phys. Lett. A 187 145). We mention a number of further results and questions concerning monotonicity of entropy and of mean entropy for more general shapes than boxes and for more general translationally invariant (/homogeneous) lattices and spaces than Z ν or R ν . We also obtain some further results on monotonicity of entropy in these more general situations by adjoining a fifth axiom, which embodies yet another general property of entropy (which we call the ‘strong triangle inequality’).
117461065
Mathematical aspects of the Hawking effect.
122974723
Linear stability of Schwarzschild under perturbations which are non-vanishing on the bifurcation 2-sphere
The authors prove boundedness on an exterior Schwarzschild wedge for Cinfinity solutions of the covariant Klein-Gordon equation which have compact support on Cauchy surfaces in Kruskal spacetime. Previously used methods enable such boundedness to be proven only for solutions whose initial data satisfy the additional restriction of vanishing at the bifurcation 2-sphere of the horizon. By employing a rarely considered discrete isometry of Kruskal spacetime and the causal propagation property of the equation, they remove this restriction. This also enables them to prove boundedness exterior to the horizon of a spacetime representing the collapse to a black hole of a spherically symmetric compact star for solutions of the same equation having Cinfinity initial data on a Cauchy surface drawn prior to the collapse.
119706030
Cross-shell excitations near the "island of inversion": Structure of Mg-30
Excited states in {sup 30}Mg have been populated to {approx}6{h_bar} and 5 MeV excitation energy with the {sup 14}C({sup 18}O,2p) reaction. Firm spin assignments for states with J>2{h_bar} have been made in this nucleus. The level scheme is compared to shell-model calculations using the Universal sd effective interaction and the Monte Carlo shell model method. Calculations employing a full sd model space fail to reproduce the observed levels. The results indicate that excitations across the N=20 gap are required at relatively low excitation energy to achieve a description of the data. The incorporation of the f{sub 7/2} and p{sub 3/2} orbitals into the model space gives improved results but indicate the need for further refinement of the models to reproduce the observed spectra.
41288355
Spectroscopy of the odd-odd fp-shell nucleus Sc-52 from secondary fragmentation
The odd-odd fp-shell nucleus {sup 52}Sc was investigated using in-beam {gamma}-ray spectroscopy following secondary fragmentation of a {sup 55}V and {sup 57}Cr cocktail beam. Aside from the known {gamma}-ray transition at 674(5) keV, a new decay at E{sub {gamma}}=212(3) keV was observed. It is attributed to the depopulation of a low-lying excited level. This new state is discussed in the framework of shell-model calculations with the GXPF1, GXPF1A, and KB3G effective interactions. These calculations are found to be fairly robust for the low-lying level scheme of {sup 52}Sc irrespective of the choice of the effective interaction. In addition, the frequency of spin values predicted by the shell model is successfully modeled by a spin distribution formulated in a statistical approach with an empirical, energy-independent spin-cutoff parameter.