Decoherence of Macroscopic Closed Systems within Newtonian Quantum Gravity

A theory recently proposed by the author aims to explain decoherence and the thermodynamical behaviour of closed systems within a conservative, unitary, framework for quantum gravity by assuming that the operators tied to the gravitational degrees of freedom are unobservable and equating physical entropy with matter-gravity entanglement entropy. Here we obtain preliminary results on the extent of decoherence this theory predicts. We treat first a static state which, if one were to ignore quantum gravitational effects, would be a quantum superposition of two spatially displaced states of a single classically well describable ball of uniform mass density in empty space. Estimating the quantum gravitational effects on this system within a simple Newtonian approximation, we obtain formulae which predict e.g. that as long as the mass of the ball is considerably larger than the Planck mass, such a would-be-coherent static superposition will actually be decohered whenever the separation of the centres of mass of the two ball-states excedes a small fraction (which decreases as the mass of the ball increases) of the ball radius. We then obtain a formula for the quantum gravitational correction to the would-be-pure density matrix of a non-relativistic many-body Schroedinger wave function and argue that this formula predicts decoherence between configurations which differ (at least) in the "relocation" of a cluster of particles of Planck mass. We estimate the entropy of some simple model closed systems, finding a tendency for it to increase with "matter-clumping" suggestive of a link with existing phenomenological discussions of cosmological entropy increase.Comment: 11 pages, plain TeX, no figures. Accepted for publication as a "Letter to the Editor" in "Classical and Quantum Gravity

Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime

We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with respect to a one-parametric family of scalar products canonically associated with the initially given one, among them being its ``purification''. As a typical example we consider a scalar field on a globally hyperbolic spacetime governed by the Klein-Gordon equation; the classical system is described by a symplectic space and the temporal evolution by symplectomorphisms (which are symplectically adjoint to their inverses). A natural scalar product is that inducing the classical energy norm, and an application of the above result yields that its ``purification'' induces on the one-particle space of the quantized system a topology which coincides with that given by the two-point functions of quasifree Hadamard states. These findings will be shown to lead to new results concerning the structure of the local (von Neumann) observable-algebras in representations of quasifree Hadamard states of the Klein-Gordon field in an arbitrary globally hyperbolic spacetime, such as local definiteness, local primarity and Haag-duality (and also split- and type III_1-properties). A brief review of this circle of notions, as well as of properties of Hadamard states, forms part of the article.Comment: 42 pages, LaTeX. The Def. 3.3 was incomplete and this has been corrected. Several misprints have been removed. All results and proofs remain unchange

The thermal and two-particle stress-energy must be ill-defined on the 2-d Misner space chronology horizon

We show that an analogue of the (four dimensional) image sum method can be used to reproduce the results, due to Krasnikov, that for the model of a real massless scalar field on the initial globally hyperbolic region IGH of two-dimensional Misner space there exist two-particle and thermal Hadamard states (built on the conformal vacuum) such that the (expectation value of the renormalised) stress-energy tensor in these states vanishes on IGH. However, we shall prove that the conclusions of a general theorem by Kay, Radzikowski and Wald still apply for these states. That is, in any of these states, for any point b on the Cauchy horizon and any neighbourhood N of b, there exists at least one pair of non-null related points (x,x'), with x and x' in the intersection of IGH with N, such that (a suitably differentiated form of) its two-point function is singular. (We prove this by showing that the two-point functions of these states share the same singularities as the conformal vacuum on which they are built.) In other words, the stress-energy tensor in any of these states is necessarily ill-defined on the Cauchy horizon.Comment: 6 pages, LaTeX, RevTeX, no figure

Brick Walls and AdS/CFT

We discuss the relationship between the bulk-boundary correspondence in Rehren's algebraic holography (and in other 'fixed-background' approaches to holography) and in mainstream 'Maldacena AdS/CFT'. Especially, we contrast the understanding of black-hole entropy from the viewpoint of QFT in curved spacetime -- in the framework of 't Hooft's 'brick wall' model -- with the understanding based on Maldacena AdS/CFT. We show that the brick-wall modification of a Klein Gordon field in the Hartle-Hawking-Israel state on 1+2-Schwarzschild AdS (BTZ) has a well-defined boundary limit with the same temperature and entropy as the brick-wall-modified bulk theory. One of our main purposes is to point out a close connection, for general AdS/CFT situations, between the puzzle raised by Arnsdorf and Smolin regarding the relationship between Rehren's algebraic holography and mainstream AdS/CFT and the puzzle embodied in the 'correspondence principle' proposed by Mukohyama and Israel in their work on the brick-wall approach to black hole entropy. Working on the assumption that similar results will hold for bulk QFT other than the Klein Gordon field and for Schwarzschild AdS in other dimensions, and recalling the first author's proposed resolution to the Mukohyama-Israel puzzle based on his 'matter-gravity entanglement hypothesis', we argue that, in Maldacena AdS/CFT, the algebra of the boundary CFT is isomorphic only to a proper subalgebra of the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of bulk and boundary theories are still the 'same' -- the total bulk state being pure, while the boundary state is mixed (thermal). We also argue from the finiteness of its boundary (and hence, on our assumptions, also bulk) entropy at finite temperature, that the Rehren dual of the Maldacena boundary CFT cannot itself be a QFT and must, instead, presumably be something like a string theory.Comment: 54 pages, 3 figures. Arguments strengthened in the light of B.S. Kay `Instability of Enclosed Horizons' arXiv:1310.739

The effect of radiative cooling on scaling laws of X-ray groups and clusters

We have performed cosmological simulations in a ΛCDM cosmology with and without radiative cooling in order to study the effect of cooling on the cluster scaling laws. Our simulations consist of 4.1 million particles each of gas and dark matter within a box size of 100 h-1 Mpc, and the run with cooling is the largest of its kind to have been evolved to z = 0. Our cluster catalogs both consist of over 400 objects and are complete in mass down to ~1013 h-1 M☉. We contrast the emission-weighted temperature-mass (Tew-M) and bolometric luminosity-temperature (Lbol-Tew) relations for the simulations at z = 0. We find that radiative cooling increases the temperature of intracluster gas and decreases its total luminosity, in agreement with the results of Pearce et al. Furthermore, the temperature dependence of these effects flattens the slope of the Tew-M relation and steepens the slope of the Lbol-Tew relation. Inclusion of radiative cooling in the simulations is sufficient to reproduce the observed X-ray scaling relations without requiring excessive nongravitational energy injection

Generating quantum states through spin chain dynamics

Spin chains can realise perfect quantum state transfer between the two ends via judicious choice of coupling strengths. In this paper, we study what other states can be created by engineering a spin chain. We conclude that, up to local phases, all single excitation quantum states with support on every site of the chain can be created. We pay particular attention to the generation of W-states that are superposed over every site of the chain.Comment: 9 pages, 1 figur

Divergences in the Effective Action for Acausal Spacetimes

The 1--loop effective Lagrangian for a massive scalar field on an arbitrary causality violating spacetime is calculated using the methods of Euclidean quantum field theory in curved spacetime. Fields of spin 1/2, spin 1 and twisted field configurations are also considered. In general, we find that the Lagrangian diverges to minus infinity at each of the nth polarised hypersurfaces of the spacetime with a structure governed by a DeWitt-Schwinger type expansion.Comment: 17 pages, Late

Universal topological phase of 2D stabilizer codes

Two topological phases are equivalent if they are connected by a local unitary transformation. In this sense, classifying topological phases amounts to classifying long-range entanglement patterns. We show that all 2D topological stabilizer codes are equivalent to several copies of one universal phase: Kitaev's topological code. Error correction benefits from the corresponding local mappings.Comment: 4 pages, 3 figure