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.
117120091
A uniqueness result for quantum field theory on spacetimes with bifurcate Killing horizons
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
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.
123597708
A uniqueness result in the Segal–Weinless approach to linear Bose fields
We prove a theorem, which, while it fits naturally into the Segal–Weinless approach to quantization seems to have been overlooked in the literature: Let (D,σ) be a symplectic space, and T (t) a one parameter group of symplectics on (D,σ). Let (H, 2Im〈⋅ ‖ ⋅〉) be a complex Hilbert space considered as a real symplectic space, and U(t) a one‐parameter unitary group on H with strictly positive energy. Suppose there is a linear symplectic map K from D to H with dense range, intertwining T (t) and U(t). Then K is unique up to unitary equivalence.
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...
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.