3,620 research outputs found
A Closed Contour of Integration in Regge Calculus
The analytic structure of the Regge action on a cone in dimensions over a
boundary of arbitrary topology is determined in simplicial minisuperspace. The
minisuperspace is defined by the assignment of a single internal edge length to
all 1-simplices emanating from the cone vertex, and a single boundary edge
length to all 1-simplices lying on the boundary. The Regge action is analyzed
in the space of complex edge lengths, and it is shown that there are three
finite branch points in this complex plane. A closed contour of integration
encircling the branch points is shown to yield a convergent real wave function.
This closed contour can be deformed to a steepest descent contour for all sizes
of the bounding universe. In general, the contour yields an oscillating wave
function for universes of size greater than a critical value which depends on
the topology of the bounding universe. For values less than the critical value
the wave function exhibits exponential behaviour. It is shown that the critical
value is positive for spherical topology in arbitrary dimensions. In three
dimensions we compute the critical value for a boundary universe of arbitrary
genus, while in four and five dimensions we study examples of product manifolds
and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra
Ions in solution: Density Corrected Density Functional Theory (DC-DFT)
Standard density functional approximations often give questionable results
for odd-electron radical complexes, with the error typically attributed to
self-interaction. In density corrected density functional theory (DC-DFT),
certain classes of density functional theory calculations are significantly
improved by using densities more accurate than the self-consistent densities.
We discuss how to identify such cases, and how DC-DFT applies more generally.
To illustrate, we calculate potential energy surfaces of HOCl and
HOHO complexes using various common approximate functionals, with
and without this density correction. Commonly used approximations yield wrongly
shaped surfaces and/or incorrect minima when calculated self consistently,
while yielding almost identical shapes and minima when density corrected. This
improvement is retained even in the presence of implicit solvent
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
Complex lapse, complex action and path integrals
Imaginary time is often used in quantum tunnelling calculations. This article
advocates a conceptually sounder alternative: complex lapse. In the ``3+1''
action for the Einstein gravitational field minimally coupled to a Klein-Gordon
field, allowing the lapse function to be complex yields a complex action which
generates both the usual Lorentzian theory and its Riemannian analogue, and in
particular allows a change of signature between the two. The action and
variational equations are manifestly well defined in the Hamiltonian
representation, with the momentum fields consequently being complex. The
complex action interpolates between the Lorentzian and Riemannian actions as
they appear formally in the respective path integrals. Thus the complex-lapse
theory provides a unified basis for a path-integral quantum theory of gravity
involving both Lorentzian and Riemannian aspects. A major motivation is the
quantum-tunnelling scenario for the origin of the universe. Taken as an
explanation for the observed quantum tunnelling of particles, the complex-lapse
theory determines that the argument of the lapse for the universe now is
extremely small but negative.Comment: 12 pages, 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
Quantum cosmology of 5D non-compactified Kaluza-Klein theory
We study the quantum cosmology of a five dimensional non-compactified
Kaluza-Klein theory where the 4D metric depends on the fifth coordinate,
. This model is effectively equivalent to a 4D non-minimally
coupled dilaton field in addition to matter generated on hypersurfaces
l=constant by the extra coordinate dependence in the four-dimensional metric.
We show that the Vilenkin wave function of the universe is more convenient for
this model as it predicts a new-born 4D universe on the constant
hypersurface.Comment: 14 pages, LaTe
Quantum cosmology with a curvature squared action
The correct quantum description for a curvature squared term in the action
can be obtained by casting the action in the canonical form with the
introduction of a variable which is the negative of the first derivative of the
field variable appearing in the action, only after removing the total
derivative terms from the action. We present the Wheeler-DeWitt equation and
obtain the expression for the probability density and current density from the
equation of continuity. Furthermore, in the weak energy limit we obtain the
classical Einstein equation. Finally we present a solution of the wave
equation.Comment: 8 pages, revte
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]
Quantum-Mechanical Histories and the Uncertainty Principle. II. Fluctuations About Classical Predictability
This paper is concerned with two questions in the decoherent histories
approach to quantum mechanics: the emergence of approximate classical
predictability, and the fluctuations about it necessitated by the uncertainty
principle. We consider histories characterized by position samplings at
moments of time. We use this to construct a probability distribution on the
value of (discrete approximations to) the field equations, , at times. We find that it is peaked around ; thus classical
correlations are exhibited. We show that the width of the peak is
largely independent of the initial state and the uncertainty principle takes
the form , where is
the width of the position samplings, and is the timescale between
projections. We determine the modifications to this result when the system is
coupled to a thermal environment. We show that the thermal fluctuations become
comparable with the quantum fluctuations under the same conditions that
decoherence effects come into play. We also study an alternative measure of
classical correlations, namely the conditional probability of finding a
sequence of position samplings, given that particular initial phase space data
have occurred. We use these results to address the issue of the formal
interpretation of the probabilities for sequences of position samplings in the
decoherent histories approach to quantum mechanics. The decoherence of the
histories is also briefly discussed.Comment: 40 pages (plain Tex), Imperial College Preprin
Chern-Simons functional and the no-boundary proposal in Bianchi IX quantum cosmology
The Chern-Simons functional is an exact solution to the
Ashtekar-Hamilton-Jacobi equation of general relativity with a nonzero
cosmological constant. In this paper we consider in Bianchi type
IX cosmology with spatial surfaces. We show that among the classical
solutions generated by~, there is a two-parameter family of
Euclidean spacetimes that have a regular NUT-type closing. When two of the
three scale factors are equal, these spacetimes reduce to a one-parameter
family within the Euclidean Taub-NUT-de~Sitter metrics. For a nonzero
cosmological constant, therefore provides a semiclassical
estimate to the Bianchi~IX no-boundary wave function in Ashtekar's variables.Comment: 9 pages, REVTeX v3.0. (One reference added.
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