2,499 research outputs found
The exact cosmological solution to the dynamical equations for the Bianchi IX model
Quantum geometrodynamics in extended phase space describes phenomenologically
the integrated system ``a physical object + observation means (a gravitational
vacuum condensate)''. The central place in this version of QGD belongs to the
Schrodinger equation for a wave function of the Universe. An exact solution to
the ``conditionally-classical'' set of equations in extended phase space for
the Bianchi-IX model and the appropriate solution to the Schrodinger equation
are considered. The physical adequacy of the obtained solutions to existing
concepts about possible cosmological scenarios is demonstrated. The
gravitational vacuum condensate is shown to be a cosmological evolution factor.Comment: LaTeX, 14 pages, to be published in Int. J. Mod. Phys.
Analytic Examples, Measurement Models and Classical Limit of Quantum Backflow
We investigate the backflow effect in elementary quantum mechanics - the
phenomenon in which a state consisting entirely of positive momenta may have
negative current and the probability flows in the opposite direction to the
momentum. We compute the current and flux for states consisting of
superpositions of gaussian wave packets. These are experimentally realizable
but the amount of backflow is small. Inspired by the numerical results of Penz
et al (M.Penz, G.Gr\"ubl, S.Kreidl and P.Wagner, J.Phys. A39, 423 (2006)), we
find two non-trivial wave functions whose current at any time may be computed
analytically and which have periods of significant backflow, in one case with a
backwards flux equal to about 70 percent of the maximum possible backflow, a
dimensionless number , discovered by Bracken and Melloy
(A.J.Bracken and G.F.Melloy, J.Phys. A27, 2197 (1994)). This number has the
unusual property of being independent of (and also of all other
parameters of the model), despite corresponding to an obviously
quantum-mechanical effect, and we shed some light on this surprising property
by considering the classical limit of backflow. We discuss some specific
measurement models in which backflow may be identified in certain measurable
probabilities.Comment: 33 pages, 14 figures. Minor revisions. Published versio
Effective Theories of Coupled Classical and Quantum Variables from Decoherent Histories: A New Approach to the Backreaction Problem
We use the decoherent histories approach to quantum theory to derive the form
of an effective theory describing the coupling of classical and quantum
variables. The derivation is carried out for a system consisting of a large
particle coupled to a small particle with the important additional feature that
the large particle is also coupled to a thermal environment producing the
decoherence necessary for classicality. The effective theory is obtained by
tracing out both the environment and the small particle variables. It consists
of a formula for the probabilities of a set of histories of the large particle,
and depends on the dynamics and initial quantum state of the small particle. It
has the form of an almost classical particle coupled to a stochastic variable
whose probabilities are determined by a formula very similar to that given by
quantum measurement theory for continuous measurements of the small particle's
position. The effective theory gives intuitively sensible answers when the
small particle is in a superposition of localized states.Comment: 27 pages, plain Te
Approximate Decoherence of Histories and 't Hooft's Deterministic Quantum Theory
This paper explores the possibility that an exactly decoherent set of
histories may be constructed from an approximately decoherent set by small
distortions of the operators characterizing the histories. In particular, for
the case of histories of positions and momenta, this is achieved by doubling
the set of operators and then finding, amongst this enlarged set, new position
and momentum operators which commute, so decohere exactly, and which are
``close'' to the original operators. The enlarged, exactly decoherent, theory
has the same classical dynamics as the original one, and coincides with the
so-called deterministic quantum theories of the type recently studied by 't
Hooft. These results suggest that the comparison of standard and deterministic
quantum theories may provide an alternative method of characterizing emergent
classicality. A side-product is the surprising result that histories of momenta
in the quantum Brownian motion model (for the free particle in the
high-temperature limit) are exactly decoherent.Comment: 41 pages, plain Te
The role of the quantum properties of gravitational radiation in the dete ction of gravitational waves
The role that the quantum properties of a gravitational wave could play in
the detection of gravitational radiation is analyzed. It is not only
corroborated that in the current laser-interferometric detectors the resolution
of the experimental apparatus could lie very far from the corresponding quantum
threshold (thus the backreaction effect of the measuring device upon the
gravitational wave is negligible), but it is also suggested that the
consideration of the quantum properties of the wave could entail the definition
of dispersion of the measurement outputs. This dispersion would be a function
not only of the sensitivity of the measuring device, but also of the
interaction time (between measuring device and gravitational radiation) and of
the arm length of the corresponding laser- interferometer. It would have a
minimum limit, and the introduction of the current experimental parameters
insinuates that the dispersion of the existing proposals could lie very far
from this minimum, which means that they would show a very large dispersion.Comment: 19 pages, Latex (use epsfig.sty
The Isaacson expansion in quantum cosmology
This paper is an application of the ideas of the Born-Oppenheimer (or
slow/fast) approximation in molecular physics and of the Isaacson (or
short-wave) approximation in classical gravity to the canonical quantization of
a perturbed minisuperspace model of the kind examined by Halliwell and Hawking.
Its aim is the clarification of the role of the semiclassical approximation and
the backreaction in such a model. Approximate solutions of the quantum model
are constructed which are not semiclassical, and semiclassical solutions in
which the quantum perturbations are highly excited.Comment: Revtex, 11 journal or 24 preprint pages. REPLACEMENT: A comment on
previous work by Dowker and Laflamme is corrected. Utah preprint
UU-REL-93/3/1
Half Quantization
A general dynamical system composed by two coupled sectors is considered. The
initial time configuration of one of these sectors is described by a set of
classical data while the other is described by standard quantum data. These
dynamical systems will be named half quantum. The aim of this paper is to
derive the dynamical evolution of a general half quantum system from its full
quantum formulation. The standard approach would be to use quantum mechanics to
make predictions for the time evolution of the half quantum initial data. The
main problem is how can quantum mechanics be applied to a dynamical system
whose initial time configuration is not described by a set of fully quantum
data. A solution to this problem is presented and used, as a guideline to
obtain a general formulation of coupled classical-quantum dynamics. Finally, a
quantization prescription mapping a given classical theory to the correspondent
half quantum one is presented.Comment: 20 pages, LaTex file, Substantially revised versio
On the interpretation of time-reparametrization-invariant quantum mechanics
The classical and quantum dynamics of simple time-reparametrization-
invariant models containing two degrees of freedom are studied in detail.
Elimination of one ``clock'' variable through the Hamiltonian constraint leads
to a description of time evolution for the remaining variable which is
essentially equivalent to the standard quantum mechanics of an unconstrained
system. In contrast to a similar proposal of Rovelli, evolution is with respect
to the geometrical proper time, and the Heisenberg equation of motion is exact.
The possibility of a ``test clock'', which would reveal time evolution while
contributing negligibly to the Hamiltonian constraint is examined, and found to
be viable in the semiclassical limit of large quantum numbers.Comment: 13 pages, set in REVTeX. One figure available by FAX from
[email protected]
Spacetime states and covariant quantum theory
In it's usual presentation, classical mechanics appears to give time a very
special role. But it is well known that mechanics can be formulated so as to
treat the time variable on the same footing as the other variables in the
extended configuration space. Such covariant formulations are natural for
relativistic gravitational systems, where general covariance conflicts with the
notion of a preferred physical-time variable. The standard presentation of
quantum mechanics, in turns, gives again time a very special role, raising well
known difficulties for quantum gravity. Is there a covariant form of
(canonical) quantum mechanics? We observe that the preferred role of time in
quantum theory is the consequence of an idealization: that measurements are
instantaneous. Canonical quantum theory can be given a covariant form by
dropping this idealization. States prepared by non-instantaneous measurements
are described by "spacetime smeared states". The theory can be formulated in
terms of these states, without making any reference to a special time variable.
The quantum dynamics is expressed in terms of the propagator, an object
covariantly defined on the extended configuration space.Comment: 20 pages, no figures. Revision: minor corrections and references
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