2,911 research outputs found

### Gravitational Radiation from a Naked Singularity -- Odd-Parity Perturbation --

It has been suggested that a naked singularity may be a good candidate for a
strong gravitational wave burster. The naked singularity occurs in the generic
collapse of an inhomogeneous dust ball. We study odd-parity mode of
gravitational waves from a naked singularity of the Lema\^{\i}tre-Tolman-Bondi
space-time. The wave equation for gravitational waves are solved by numerical
integration using the single null coordinate. The result is that the naked
singularity is not a strong source of the odd-parity gravitational radiation
although the metric perturbation grows in the central region. Therefore, the
Cauchy horizon in this space-time would be marginally stable against odd-parity
perturbations.Comment: 14 pages, 7 figures, to be published in Prog. Theor. Phys. Final
version, with minor changes. Reference 13 adde

### Gravitational Radiation from a Naked Singularity. II - Even-Parity Perturbation -

A naked singularity occurs in the generic collapse of an inhomogeneous dust
ball. We study the even-parity mode of gravitational waves from a naked
singularity of the Lema\^{\i}tre-Tolman-Bondi spacetime. The wave equations for
gravitational waves are solved by numerical integration using the single null
coordinate. The result implies that the metric perturbation grows when it
approaches the Cauchy horizon and diverges there, although the naked
singularity is not a strong source of even-parity gravitational radiation.
Therefore, the Cauchy horizon in this spacetime should be unstable with respect
to linear even-parity perturbations.Comment: 16 pages, 5 figures, errors and typos corrected, final versio

### Physical Processes in Naked Singularity Formation

Gravitational collapse is one of the most fruitful subjects in gravitational
physics. It is well known that singularity formation is inevitable in complete
gravitational collapse. It was conjectured that such a singularity should be
hidden by horizons if it is formed from generic initial data with physically
reasonable matter fields. Many possible counterexamples to this conjecture have
been proposed over the past three decades, although none of them has proved to
be sufficiently generic. In these examples, there appears a singularity that is
not hidden by horizons. This singularity is called a `naked singularity.' The
appearance of a naked singularity represents the formation of an observable
high-curvature, strong-gravity region. In this paper we review examples of
naked singularity formation and recent progress in research of observable
physical processes - gravitational radiation and quantum particle creation -
from a forming naked singularity.Comment: 76 pages, 25 figure file

### General Connectivity Distribution Functions for Growing Networks with Preferential Attachment of Fractional Power

We study the general connectivity distribution functions for growing networks
with preferential attachment of fractional power, $\Pi_{i} \propto k^{\alpha}$,
using the Simon's method. We first show that the heart of the previously known
methods of the rate equations for the connectivity distribution functions is
nothing but the Simon's method for word problem. Secondly, we show that the
case of fractional $\alpha$ the $Z$-transformation of the rate equation
provides a fractional differential equation of new type, which coincides with
that for PA with linear power, when $\alpha = 1$. We show that to solve such a
fractional differential equation we need define a transidental function
$\Upsilon (a,s,c;z)$ that we call {\it upsilon function}. Most of all
previously known results are obtained consistently in the frame work of a
unified theory.Comment: 10 page

### Partial and macroscopic phase coherences in underdoped Bi${}_{2}$Sr${}_{2}$CaCu${}_{2}$O${}_{8+{\delta}}$ thin film

A combined study with use of time-domain pump-probe spectroscopy and
time-domain terahertz transmission spectroscopy have been carried out on an
underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+{\delta}}$ thin film. It was observed that
the low energy multi-excitation states were decomposed into superconducting gap
and pseudogap. The pseudogap locally opens below $T^*{\simeq}210$ K
simultaneously with the appearance of the high-frequency partial pairs around
1.3 THz. With decreasing temperature, the number of the local domains with the
partial phase coherence increased and saturated near 100 K, and the macroscopic
superconductivity appeared below 76 K through the superconductivity fluctuation
state below 100 K. These experimental results indicate that the pseudogap makes
an important role for realization of the superconductivity as a precursor to
switch from the partial to the macroscopic phase coherence.Comment: Revtex4, 4 pages, 4 figure

### Classical no-cloning theorem under Liouville dynamics by non-Csisz\'ar f-divergence

The Csisz\'ar f-divergence, which is a class of information distances, is
known to offer a useful tool for analysing the classical counterpart of the
cloning operations that are quantum mechanically impossible for the factorized
and marginality classical probability distributions under Liouville dynamics.
We show that a class of information distances that does not belong to this
divergence class also allows for the formulation of a classical analogue of the
quantum no-cloning theorem. We address a family of nonlinear Liouville-like
equations, and generic distances, to obtain constraints on the corresponding
functional forms, associated with the formulation of classical analogue of the
no-cloning principle.Comment: 6 pages, revised, published versio

### Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems

A criterion to determine the existence of zero-energy edge states is
discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a
parameter space is assigned for each one-dimensional bulk Hamiltonian, and its
topological properties, combined with the chiral symmetry, play an essential
role. It provides a unified framework to discuss zero-energy edge modes for
several systems such as fully gapped superconductors, two-dimensional d-wave
superconductors, and graphite ribbons. A variants of the Peierls instability
caused by the presence of edges is also discussed.Comment: Completely rewritten. Discussions on coexistence of is- or
id_{xy}-wave order parameter near edges in d_{x^{2}-y^{2}}-wave
superconductors are added; 4 pages, 3 figure

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