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’).
123297693
Sufficient conditions for quasifree states and an improved uniqueness theorem for quantum fields on space–times with horizons
Let ω be a state on the Weyl algebra over a symplectic space. We prove that if either (i) the ‘‘liberation’’ of ω is pure or (ii) the restriction of ω to each of two generating Weyl subalgebras is quasifree and pure, then ω is quasifree and pure [and, in case (i) is equal to its liberation, in case (ii) is uniquely determined by its restrictions]. [Here, we define the liberation of a (sufficiently regular) state to be the quasifree state with the same two point function.] Results (i) and (ii) permit one to drop the quasifree assumption in a result due to Wald and the author concerning linear scalar quantum fields on space–times with bifurcate Killing horizons and thus to conclude that, on a large subalgebra of the field algebra for such a system, there is a unique stationary state whose two point function has the Hadamard form. The paper contains a number of further related developments including: (a) (i) implies a uniqueness result, e.g., for the usual free field in Minkowski space. We compare and contra...
55078864
Classical wave operators and asymptotic quantum field operators on curved space-times
We consider a class of Lorentzian metrics on ~4 which are stationary at time-like infinity and Minkowskian either at space-like or time-like infinity. For these metrics, we construct wave operators for the classical Klein-Gordon equation. For certain transient cases we also construct inverse wave operators. Given the classical wave operators, we show how to construct in and out field operators for the quantum Klein-Gordon equation and a particle interpretation for this theory. Finally, we give several results of a general nature on the construction of classical and quantum scattering operators paying special attention to the stationary case. The methods and results of the paper could be generalized to other external field problems (not just gravitational). RESUME. Nous considerons une classe de metriques lorentziennes sur [R4 stationnaires a l’infini temporel et minkowskiennes a l’infini spatial ou a l’infini temporel. Dans ces metriques, nous construisons des (*) Supported by National Science Foundation grant PHY8001658. (**) Supported by British Science Research Council under contract GR/A/61463, and by Schweizerischer Nationalfonds. Annales de l’Institut Henri Poincaré-Section A-Vol. XXXVII, 0020-2339/1982/ 93 /$ 5,00/ ~ Gauthier-Villars 4 94 J. DIMOCK AND B. S. KAY operateurs d’onde pour 1’equation de Klein-Gordon classique. Pour certains cas de champs gravitationnels ephemeres, nous construisons aussi les operateurs d’onde inverses. Les operateurs d’onde classiques etant donnes, nous expliquons comment construire des operateurs de champs in et out pour 1’equation de Klein-Gordon quantique et obtenons une interpretation en termes de particules pour cette theorie. Finalement, nous demontrons plusieurs resultats de nature plus generate concernant la construction d’operateurs de diffusion en développant particulierement Ie cas stationnaire. On pourrait generaliser les methodes et resultats de cet article a d’autres problemes de champs externes (non seulement gravitationnels).
16748405
The robustness of a many-body decoherence formula of Kay under changes in graininess and shape of the bodies
In "Decoherence of macroscopic closed systems within Newtonian quantum gravity" (Kay B S 1998 Class. Quantum Grav. 15 L89-L98) it was argued that, given a many-body Schrodinger wave function ψ(x1, . . . , xN) for the centre-of- mass degrees of freedom of a closed system of N identical uniform-mass balls of mass M and radius R, taking account of quantum gravitational effects and then tracing over the gravitational field amounts to multiplying the position-space density matrix
117120091
A uniqueness result for quantum field theory on spacetimes with bifurcate Killing horizons
120462489
Boundary conditions for quantum mechanics on cones and fields around cosmic strings
We study the options for boundary conditions at the conical singularity for quantum mechanics on a two-dimensional cone with deficit angle ≦ 2π and for classical and quantum scalar fields propagating with a translationally invariant dynamics in the 1+3 dimensional spacetime around an idealized straight infinitely long, infinitesimally thin cosmic string. The key to our analysis is the observation that minus-the-Laplacian on a cone possesses a one-parameter family of selfadjoint extensions. These may be labeled by a parameterR with the dimensions of length—taking values in [0, ∞). ForR=0, the extension is positive. WhenR≠0 there is a bound state. Each of our problems has a range of possible dynamical evolutions corresponding to a range of allowedR-values. They correspond to either finite, forR=0, or logarithmically divergent, forR≠0, boundary conditions at zero radius. Non-zeroR-values are a satisfactory replacement for the (mathematically ill-defined) notion of δ-function potentials at the cone's apex.We discuss the relevance of the various idealized dynamics to quantum mechanics on a cone with a rounded-off centre and field theory around a “true” string of finite thickness. Provided one is interested in effects at sufficiently large length scales, the “true” dynamics will depend on the details of the interaction of the wave function with the cone's centre (/field with the string etc.) only through a single parameterR (its “scattering length”) and will be well-approximated by the dynamics for the corresponding idealized problem with the sameR-value. This turns out to be zero if the interaction with the centre is purely gravitational and minimally coupled, but non-zero values can be important to model nongravitational (or non-minimally coupled) interactions. Especially, we point out the relevance of non-zeroR-values to electromagnetic waves around superconducting strings. We also briefly speculate on the relevance of theR-parameter in the application of quantum mechanics on cones to 1+2 dimensional quantum gravity with massive scalars.
118976996
One-neutron knockout in the vicinity of the N=32 sub-shell closure: Be-9(Cr-57,Cr-56+gamma)X
Gade, A. Janssens, R. V. F. Bazin, D. Brown, B. A. Campbell, C. M. Carpenter, M. P. Cook, J. M. Deacon, A. N. Dinca, D. -C. Freeman, S. J. Glasmacher, T. Horoi, M. Kay, B. P. Mantica, P. F. Mueller, W. F. Terry, J. R. Tostevin, J. A. Zhu, S.
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.