42 research outputs found
Smearing effect due to the spread of a probe-particle on the Brownian motion near a perfectly reflecting boundary
Quantum fluctuations of electromagnetic vacuum are investigated in a
half-space bounded by a perfectly reflecting plate by introducing a probe
described by a charged wave-packet distribution in time-direction. The
wave-packet distribution of the probe enables one to investigate the smearing
effect upon the measured vacuum fluctuations caused by the quantum nature of
the probe particle. It is shown that the wave-packet spread of the probe
particle significantly influences the measured velocity dispersion of the
probe. In particular, the asymptotic late-time behavior of its -component, , for the wave-packet case is quite different from the test
point-particle case ( is the coordinate normal to the plate). The result for
the wave-packet is \sim 1/\t^2 in the late time (\t is the
measuring time), in stead of the reported late-time behavior for a point-particle probe. This result can be quite significant
for further investigations on the measurement of vacuum fluctuations.Comment: 8 page
Evolution of the discrepancy between a universe and its model
We study a fundamental issue in cosmology: Whether we can rely on a
cosmological model to understand the real history of the Universe. This
fundamental, still unresolved issue is often called the ``model-fitting problem
(or averaging problem) in cosmology''. Here we analyze this issue with the help
of the spectral scheme prepared in the preceding studies.
Choosing two specific spatial geometries that are very close to each other,
we investigate explicitly the time evolution of the spectral distance between
them; as two spatial geometries, we choose a flat 3-torus and a perturbed
geometry around it, mimicking the relation of a ``model universe'' and the
``real Universe''. Then we estimate the spectral distance between them and
investigate its time evolution explicitly. This analysis is done efficiently by
making use of the basic results of the standard linear structure-formation
theory.
We observe that, as far as the linear perturbation of geometry is valid, the
spectral distance does not increase with time prominently,rather it shows the
tendency to decrease. This result is compatible with the general belief in the
reliability of describing the Universe by means of a model, and calls for more
detailed studies along the same line including the investigation of wider class
of spacetimes and the analysis beyond the linear regime.Comment: To be published in Classical and Quantum Gravit
Switching effect upon the quantum Brownian motion near a reflecting boundary
The quantum Brownian motion of a charged particle in the electromagnetic
vacuum fluctuations is investigated near a perfectly reflecting flat boundary,
taking into account the smooth switching process in the measurement.
Constructing a smooth switching function by gluing together a plateau and the
Lorentzian switching tails, it is shown that the switching tails have a great
influence on the measurement of the Brownian motion in the quantum vacuum.
Indeed, it turns out that the result with a smooth switching function and the
one with a sudden switching function are qualitatively quite different. It is
also shown that anti-correlations between the switching tails and the main
measuring part plays an essential role in this switching effect. The switching
function can also be interpreted as a prototype of an non-equilibrium process
in a realistic measurement, so that the switching effect found here is expected
to be significant in actual applications in vacuum physics.Comment: 12 pages, 2 figures This version is just to correct the author-lis
Dynamical Evolution of a Cylindrical Shell with Rotational Pressure
We prepare a general framework for analyzing the dynamics of a cylindrical
shell in the spacetime with cylindrical symmetry. Based on the framework, we
investigate a particular model of a cylindrical shell-collapse with rotational
pressure, accompanying the radiation of gravitational waves and massless
particles. The model has been introduced previously but has been awaiting for
proper analysis. Here the analysis is put forward: It is proved that, as far as
the weak energy condition is satisfied outside the shell, the collapsing shell
bounces back at some point irrespective of the initial conditions, and escapes
from the singularity formation.
The behavior after the bounce depends on the sign of the shell pressure in
the z-direction. When the pressure is non-negative, the shell continues to
expand without re-contraction. On the other hand, when the pressure is negative
(i.e. it has a tension), the behavior after the bounce can be more complicated
depending on the details of the model. However, even in this case, the shell
never reaches the zero-radius configuration.Comment: To appear in Phys. Rev.
Relativistic dynamics of cylindrical shells of counter-rotating particles
Although infinite cylinders are not astrophysical entities, it is possible to
learn a great deal about the basic qualitative features of generation of
gravitational waves and the behavior of the matter conforming such shells in
the limits of very small radius. We describe the analytical model using kinetic
theory for the matter and the junction conditions through the shell to obtain
its equation of motion. The nature of the static solutions are analyzed, both
for a single shell as well as for two concentric shells. In this second case,
for a time dependent external shell, we integrate numerically the equation of
motion for several values of the constants of the system. Also, a brief
description in terms of the Komar mass is given to account for the
gravitational wave energy emitted by the system.Comment: 19 pages, 8 figure
The spectral representation of the spacetime structure: The `distance' between universes with different topologies
We investigate the representation of the geometrical information of the
universe in terms of the eigenvalues of the Laplacian defined on the universe.
We concentrate only on one specific problem along this line: To introduce a
concept of distance between universes in terms of the difference in the
spectra.
We can find out such a measure of closeness from a general discussion. The
basic properties of this `spectral distance' are then investigated. It can be
related to a reduced density matrix element in quantum cosmology. Thus,
calculating the spectral distance gives us an insight for the quantum
theoretical decoherence between two universes. The spectral distance does not
in general satisfy the triangular inequality, illustrating that it is not
equivalent to the distance defined by the DeWitt metric on the superspace.
We then pose a question: Whether two universes with different topologies
interfere with each other quantum mechanically? We concentrate on the
difference in the orientabilities. Several concrete models in 2-dimension are
set up, and the spectral distances between them are investigated: Tori and
Klein's bottles, spheres and real projective spaces. Quite surprisingly, we
find many cases of spaces with different orientabilities in which the spectral
distance turns out to be very short. It may suggest that, without any other
special mechanism, two such universes interfere with each other quite strongly.Comment: 47 page
Can the entanglement entropy be the origin of black-hole entropy ?
Entanglement entropy is often speculated as a strong candidate for the origin
of the black-hole entropy. To judge whether this speculation is true or not, it
is effective to investigate the whole structure of thermodynamics obtained from
the entanglement entropy, rather than just to examine the apparent structure of
the entropy alone or to compare it with that of the black hole entropy. It is
because entropy acquires a physical significance only when it is related to the
energy and the temperature of a system. From this point of view, we construct a
`thermodynamics of entanglement' by introducing an entanglement energy and
compare it with the black-hole thermodynamics. We consider two possible
definitions of entanglement energy. Then we construct two different kinds of
thermodynamics by combining each of these different definitions of entanglement
energy with the entanglement entropy. We find that both of these two kinds of
thermodynamics show significant differences from the black-hole thermodynamics
if no gravitational effects are taken into account. These differences are in
particular highlighted in the context of the third law of thermodynamics.
Finally we see how inclusion of gravity alter the thermodynamics of the
entanglement. We give a suggestive argument that the thermodynamics of the
entanglement behaves like the black-hole thermodynamics if the gravitational
effects are included properly. Thus the entanglement entropy passes a
non-trivial check to be the origin of the black-hole entropy.Comment: 40 pages, Latex file, one figur
Thermodynamics of entanglement in Schwarzschild spacetime
Extending the analysis in our previous paper, we construct the entanglement
thermodynamics for a massless scalar field on the Schwarzschild spacetime.
Contrary to the flat case, the entanglement energy turns out to be
proportional to area radius of the boundary if it is near the horizon. This
peculiar behavior of can be understood by the red-shift effect caused
by the curved background. Combined with the behavior of the entanglement
entropy, this result yields, quite surprisingly, the entanglement
thermodynamics of the same structure as the black hole thermodynamics. On the
basis of these results, we discuss the relevance of the concept of entanglement
as the microscopic origin of the black hole thermodynamics.Comment: 27 pages, Latex file, 7 figures; revised to clarify our choice of the
state and to add references. Accepted for publication in Physical Review
Detection of minimal residual disease identifies differences in treatment response between T-ALL and precursor B-ALL
We performed sensitive polymerase chain reaction-based minimal residual
disease (MRD) analyses on bone marrow samples at 9 follow-up time points
in 71 children with T-lineage acute lymphoblastic leukemia (T-ALL) and
compared the results with the precursor B-lineage ALL (B-ALL) results (n =
210) of our previous study. At the first 5 follow-up time points, the
frequency of MRD-positive patients and the MRD levels were higher in T-ALL
than in precursor-B-ALL, reflecting the more frequent occurrence of
resistant disease in T-ALL. Subsequently, patients were classified
according to their MRD level at time point 1 (TP1), taken at the end of
induction treatment (5 weeks), and at TP2 just before the start of
consolidation treatment (3 months). Patients were considered at low risk
if TP1 and TP2 were MRD negative and at high risk if MRD levels at TP1 and
TP2 were 10(-3) or higher; remaining patients were considered at
intermediate risk. The relative distribution of patients with T-ALL (n =
43) over the MRD-based risk groups differed significantly from that of
precursor B-ALL (n = 109). Twenty-three percent of patients with T-ALL and
46% of patients with precursor B-ALL were classified in the low-risk group
(P =.01) and had a 5-year relapse-free survival (RFS) rate of 98% or
greater. In contrast, 28% of patients with T-ALL were classified in the
MRD-based high-risk group compared to only 11% of patients with precursor
B-ALL (P =.02), and the RFS rates were 0% and 25%, respectively (P =.03).
Not only was the distribution of patients with T-ALL different over the
MRD-based risk groups, the prognostic value of MRD levels at TP1 and TP2
was higher in T-ALL (larger RFS gradient), and consistently higher RFS
rates were found for MRD-negative T-ALL patients at the first 5 follow-up
time points
Euclidean Supergravity in Terms of Dirac Eigenvalues
It has been recently shown that the eigenvalues of the Dirac operator can be
considered as dynamical variables of Euclidean gravity. The purpose of this
paper is to explore the possiblity that the eigenvalues of the Dirac operator
might play the same role in the case of supergravity. It is shown that for this
purpose some primary constraints on covariant phase space as well as secondary
constraints on the eigenspinors must be imposed. The validity of primary
constraints under covariant transport is further analyzed. It is show that in
the this case restrictions on the tanget bundle and on the spinor bundle of
spacetime arise. The form of these restrictions is determined under some
simplifying assumptions. It is also shown that manifolds with flat curvature of
tangent bundle and spinor bundle and spinor bundle satisfy these restrictons
and thus they support the Dirac eigenvalues as global observables.Comment: Misprints and formulae corrected; to appear in Phys. Rev.