71 research outputs found
Black hole and baby universe in a thin film of 3He-A
Condensed matter black hole analogues may provide guidance in grappling with
difficult questions about the role of short distance physics in the Hawking
effect. These questions bear on the very existence of Hawking radiation, the
correlations it may or may not carry, the nature of black hole entropy, and the
possible loss of information when a black hole evaporates. We describe a model
of black hole formation and evaporation and the loss of information to a
disconnected universe in a thin film of 3He-A, and we explain why the existence
of Hawking radiation has not yet been demonstrated in this model. [We would
like this article to be accessible to researchers in both condensed matter and
gravitational physics, hence we include more than the usual amount of
introductory material.]Comment: 21 pages, Chapter for book, "Artificial Black Holes", eds. M.
Novello, M. Visser, and G. Volovik (World Scientific, 2002), based on a talk
by TJ at the Workshop on Analog Models of General Relativity, held at CBPF in
Rio de Janeiro, October 16-20, 200
Disturbance by optimal discrimination
We discuss the disturbance by measurements which unambiguously discriminate
between given candidate states. We prove that such an optimal measurement
necessarily changes distinguishable states indistinguishable when the
inconclusive outcome is obtained. The result was previously shown by
Chefles~[Phys. Lett. A 239, 339 (1998)] under restrictions on the class of
quantum measurements and on the definition of optimality. Our theorems remove
these restrictions and are also applicable to infinitely many candidate states.
Combining with our previous results, one can obtain concrete mathematical
conditions for the resulting states. The method may have a wide variety of
applications in contexts other than state discrimination
Big bounce as scattering of wave function at big crunch
A gauge-invariant quantum theory of the Friedmann-Robertson-Walker (FRW)
universe with dust is studied in terms of the Ashtekar variables. We use the
reduced phase space quantization which has following advantages: (i)
fundamental variables are all gauge invariant, (ii) there exists a physical
time evolution of gauge-invariant quantities, so that the problem of time is
absent and (iii) the reduced phase space can be quantized in the same manner as
in ordinary quantum mechanics. In the FRW model, the dynamical components of
the Ashtekar variables are given by a single quantity and its conjugate
momentum, where is related to the scale factor as
and its sign gives the orientation of triads. We solve a scattering problem in
terms of ingoing and outgoing energy eigenstates. We show that the incident
wave is reflected in rate and transmitted in rate at the classical
singularity . Analyzing the dynamics of a wave packet, we show that the
classical initial singularity is replaced by a big bounce in quantum theory. A
possible interpretation of the result is that the wave function of the universe
has been in a superposition of states representing right-handed and left-handed
systems before the big bounce.Comment: 9 pages, 4 figure
Gauge-invariant construction of quantum cosmology
We present and analyze a gauge-invariant quantum theory of the
Friedmann-Robertson-Walker universe with dust. We construct the reduced phase
space spanned by gauge-invariant quantities by using the so-called relational
formalism at the classical level. The reduced phase space thereby obtained can
be quantized in the same manner as an ordinary mechanical system. We carry out
the quantization and obtain the Schr\"{o}dinger equation. This quantization
procedure realizes a possible resolution to the problem of time and observables
in canonical quantum gravity. We analyze the classical initial singularity of
the theory by evolving a wave packet backward in time and evaluating the
expectation value of the scale factor. It is shown that the initial singularity
of the Universe is avoided by the quantum gravitational effects.Comment: 8 pages, 7 figures, accepted for publication in Phys. Rev.
Causal Feature of Central Singularity and Gravitational Mass
Mass of singularity is defined, and its relation to whether the singularity
is spacelike, timelike or null is discussed for spherically symmetric
spacetimes.
It is shown that if the mass of singularity is positive
(negative) the singularity is non-timelike (non-spacelike).
The connection between the sign of the mass and the force on a particle is
also discussed.Comment: 10 pages REVTeX 3.0, TIT/HEP-246/COSMO-4
Hamiltonian structures for compact homogeneous universes
Hamiltonian structures for spatially compact locally homogeneous vacuum
universes are investigated, provided that the set of dynamical variables
contains the \Teich parameters, parameterizing the purely global geometry. One
of the key ingredients of our arguments is a suitable mathematical expression
for quotient manifolds, where the universal cover metric carries all the
degrees of freedom of geometrical variations, i.e., the covering group is
fixed. We discuss general problems concerned with the use of this expression in
the context of general relativity, and demonstrate the reduction of the
Hamiltonians for some examples. For our models, all the dynamical degrees of
freedom in Hamiltonian view are unambiguously interpretable as geometrical
deformations, in contrast to the conventional open models.Comment: 27 pages including 2 figures. REVTeX and epsf package
Hamiltonians for Compact Homogeneous Universes
We briefly show how we can obtain Hamiltonians for spatially compact locally
homogeneous vacuum spacetimes. The dynamical variables are categorized into the
curvature parameters and the Teichm\"{u}ller parameters. While the
Teichm\"{u}ller parameters usually parameterise the covering group of the
spatial sections, we utilise another suitable parameterization where the
universal cover metric carries all the dynamical variables and with this we
reduce the Hamiltonians. For our models, all dynamical variables possess their
clear geometrical meaning, in contrast to the conventional open models.}Comment: 3 pages, LaTeX, uses mprocl.sty. Talk given at the Eighth Marcel
Grossmann Meeting on General Relativity, 22-27 June 1997, Jerusale
Renormalization group and critical behaviour in gravitational collapse
We present a general framework for understanding and analyzing critical
behaviour in gravitational collapse. We adopt the method of renormalization
group, which has the following advantages. (1) It provides a natural
explanation for various types of universality and scaling observed in numerical
studies. In particular, universality in initial data space and universality for
different models are understood in a unified way. (2) It enables us to perform
a detailed analysis of time evolution beyond linear perturbation, by providing
rigorous controls on nonlinear terms. Under physically reasonable assumptions
we prove: (1) Uniqueness of the relevant mode around a fixed point implies
universality in initial data space. (2) The critical exponent and
the unique positive eigenvalue of the relevant mode is exactly related
by , where is a scaling exponent. (3) The
above (1) and (2) hold also for discretely self-similar case (replacing ``fixed
point'' with ``limit cycle''). (4) Universality for diffent models holds under
a certain condition.
According to the framework, we carry out a rather complete (though not
mathematically rigorous) analysis for perfect fluids with pressure proportional
to density, in a wide range of the adiabatic index . The uniqueness of
the relevant mode around a fixed point is established by Lyapunov analyses.
This shows that the critical phenomena occurs not only for the radiation fluid
but also for perfect fluids with . The accurate
values of critical exponents are calculated for the models.Comment: ReVTeX, 42 pages with 8 embedded PS figures using "boxedeps.tex."
This is a replacement, which (1) presents more straightforward presentation
by sending some detailed "proofs" into the appendices, (2) corrects some
minor errors in the first versio
Killing Tensors and Conserved Quantities of a Relativistic Particle in External Fields
We generalize Killing equations to a test particle system which is subjected
to external force. We relax the conservation condition by virtue of
reparametrization invariance of a particle orbit. As a result, we obtain
generalized Killing equations which have hierarchical structure on the top of
which a conformal Killing equation exists.Comment: Proceedings of the 12th Marcel Grossmann Meeting on General
Relativity (MG 12), Paris, France, 12-18 Jul 200
State protection by quantum control before and after noise
We discuss the possibility of protecting the state of a quantum system that
goes through noise by measurements and operations before and after the noise
process. We extend our previous result on nonexistence of "truly quantum"
protocols that protect an unknown qubit state against the depolarizing noise
better than "classical" ones [Phys. Rev. A, 95, 022321 (2017)] in two
directions. First, we show that the statement is also true in any
finite-dimensional Hilbert spaces, which was previously conjectured, the
optimal protocol is either the do nothing protocol or the discriminate and
reprepare protocol, depending on the strength of the noise. Second, in the case
of a qubit, we show that essentially the same conclusion holds for any unital
noise. These results describe the fundamental limitations in quantum mechanics
from the viewpoint of control theory.Comment: 8 pages, 2 figure
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