848 research outputs found
A Perturbative Approach to the Relativistic Harmonic Oscillator
A quantum realization of the Relativistic Harmonic Oscillator is realized in
terms of the spatial variable and {\d\over \d x} (the minimal canonical
representation). The eigenstates of the Hamiltonian operator are found (at
lower order) by using a perturbation expansion in the constant . Unlike
the Foldy-Wouthuysen transformed version of the relativistic hydrogen atom,
conventional perturbation theory cannot be applied and a perturbation of the
scalar product itself is required.Comment: 9 pages, latex, no figure
A robust pseudo-inverse spectral filter applied to the Earth Radiation Budget Experiment (ERBE) scanning channels
Computer simulations of a least squares estimator operating on the ERBE scanning channels are discussed. The estimator is designed to minimize the errors produced by nonideal spectral response to spectrally varying and uncertain radiant input. The three ERBE scanning channels cover a shortwave band a longwave band and a ""total'' band from which the pseudo inverse spectral filter estimates the radiance components in the shortwave band and a longwave band. The radiance estimator draws on instantaneous field of view (IFOV) scene type information supplied by another algorithm of the ERBE software, and on a priori probabilistic models of the responses of the scanning channels to the IFOV scene types for given Sun scene spacecraft geometry. It is found that the pseudoinverse spectral filter is stable, tolerant of errors in scene identification and in channel response modeling, and, in the absence of such errors, yields minimum variance and essentially unbiased radiance estimates
Quantisation of Conformal Fields in Three-dimensional Anti-de Sitter Black Hole Spacetime
Utilizing the conformal-flatness nature of 3-dim. Anti-de Sitter (AdS_3)
black hole solution of Banados, Teitelboim and Zanelli, the quantisation of
conformally-coupled scalar and spinor fields in this background spacetime is
explicitly carried out. In particular, mode expansion forms and propagators of
the fields are obtained in closed forms. The vacuum in this conformally-coupled
field theories in AdS_3 black hole spacetime, which is conformally-flat, is the
conformal vacuum which is unique and has global meaning. This point
particularly suggests that now the particle production by AdS_3 black hole
spacetime should be absent. General argument establishing the absence of real
particle creation by AdS_3 black hole spacetime for this case of conformal
triviality is provided. Then next, using the explicit mode expansion forms for
conformally-coupled scalar and spinor fields, the bosonic and fermionic
superradiances are examined and found to be absent confirming the expectation.Comment: 51 pages, Revtex, version to appear in Int. J. Mod. Phys.
On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables
In this paper we explore further the connections between convex bodies
related to quantum correlation experiments with dichotomic variables and
related bodies studied in combinatorial optimization, especially cut polyhedra.
Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J.
Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show
that several well known bodies related to cut polyhedra are equivalent to
bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to
represent hidden deterministic behaviors, quantum behaviors, and no-signalling
behaviors. Among other things, our results allow a unique representation of
these bodies, give a necessary condition for vertices of the no-signalling
polytope, and give a method for bounding the quantum violation of Bell
inequalities by means of a body that contains the set of quantum behaviors.
Optimization over this latter body may be performed efficiently by semidefinite
programming. In the second part of the paper we apply these results to the
study of classical correlation functions. We provide a complete list of tight
inequalities for the two party case with (m,n) dichotomic observables when
m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation
inequalities.Comment: 17 pages, 2 figure
Quantum correlations in the temporal CHSH scenario
We consider a temporal version of the CHSH scenario using projective
measurements on a single quantum system. It is known that quantum correlations
in this scenario are fundamentally more general than correlations obtainable
with the assumptions of macroscopic realism and non-invasive measurements. In
this work, we also educe some fundamental limitations of these quantum
correlations. One result is that a set of correlators can appear in the
temporal CHSH scenario if and only if it can appear in the usual spatial CHSH
scenario. In particular, we derive the validity of the Tsirelson bound and the
impossibility of PR-box behavior. The strength of possible signaling also turns
out to be surprisingly limited, giving a maximal communication capacity of
approximately 0.32 bits. We also find a temporal version of Hardy's nonlocality
paradox with a maximal quantum value of 1/4.Comment: corrected versio
Back-reaction of a conformal field on a three-dimensional black hole
The first order corrections to the geometry of the (2+1)-dimensional black
hole due to back-reaction of a massless conformal scalar field are computed.
The renormalized stress energy tensor used as the source of Einstein equations
is computed with the Green function for the black-hole background with
transparent boundary conditions. This tensor has the same functional form as
the one found in the nonperturbative case which can be exactly solved. Thus, a
static, circularly symmetric and asymptotically anti-de Sitter black hole
solution of the semiclassical equations is found. The corrections to the
thermodynamic quantities are also computed.Comment: 12 pages, RevTeX, no figure
Entropy of scalar fields in 3+1 dimensional constant curvature black hole background
We consider the thermodynamics of minimally coupled massive scalar field in
3+1 dimensional constant curvature black hole background. The brick wall model
of 't Hooft is used. When Scharzschild like coordinates are used it is found
that apart from the usual radial brick wall cut-off parammeter an angular
cut-off parameter is required to regularize the solution. Free energy of the
scalar field is obtained through counting of states using the WKB
approximation. It is found that the free energy and the entropy are
logarithmically divergent in both the cut-off parameters.Comment: 9 pages, LaTe
Polyhedral Analysis using Parametric Objectives
The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output
Stability of degenerate Cauchy horizons in black hole spacetimes
In the multihorizon black hole spacetimes, it is possible that there are
degenerate Cauchy horizons with vanishing surface gravities. We investigate the
stability of the degenerate Cauchy horizon in black hole spacetimes. Despite
the asymptotic behavior of spacetimes (flat, anti-de Sitter, or de Sitter), we
find that the Cauchy horizon is stable against the classical perturbations, but
unstable quantum mechanically.Comment: Revtex, 4 pages, no figures, references adde
Quantum scalar field on three-dimensional (BTZ) black hole instanton: heat kernel, effective action and thermodynamics
We consider the behaviour of a quantum scalar field on three-dimensional
Euclidean backgrounds: Anti-de Sitter space, the regular BTZ black hole
instanton and the BTZ instanton with a conical singularity at the horizon. The
corresponding heat kernel and effective action are calculated explicitly for
both rotating and non-rotating holes. The quantum entropy of the BTZ black hole
is calculated by differentiating the effective action with respect to the
angular deficit at the conical singularity. The renormalization of the
UV-divergent terms in the action and entropy is considered. The structure of
the UV-finite term in the quantum entropy is of particular interest. Being
negligible for large outer horizon area it behaves logarithmically for
small . Such behaviour might be important at late stages of black hole
evaporation.Comment: 28 pages, latex, 2 figures now include
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