665 research outputs found
Some properties of the resonant state in quantum mechanics and its computation
The resonant state of the open quantum system is studied from the viewpoint
of the outgoing momentum flux. We show that the number of particles is
conserved for a resonant state, if we use an expanding volume of integration in
order to take account of the outgoing momentum flux; the number of particles
would decay exponentially in a fixed volume of integration. Moreover, we
introduce new numerical methods of treating the resonant state with the use of
the effective potential. We first give a numerical method of finding a
resonance pole in the complex energy plane. The method seeks an energy
eigenvalue iteratively. We found that our method leads to a super-convergence,
the convergence exponential with respect to the iteration step. The present
method is completely independent of commonly used complex scaling. We also give
a numerical trick for computing the time evolution of the resonant state in a
limited spatial area. Since the wave function of the resonant state is
diverging away from the scattering potential, it has been previously difficult
to follow its time evolution numerically in a finite area.Comment: 20 pages, 12 figures embedde
A note on a local ergodic theorem for an infinite tower of coverings
This is a note on a local ergodic theorem for a symmetric exclusion process
defined on an infinite tower of coverings, which is associated with a finitely
generated residually finite amenable group.Comment: Final version to appear in Springer Proceedings in Mathematics and
Statistic
Pattern formation in crystal growth under parabolic shear flow
Morphological instability of the solid-liquid interface occuring in a crystal
growing from an undercooled thin liquid being bounded on one side by a free
surface and flowing down inclined plane is investigated by a linear stability
analysis under shear flow. It is found that restoring forces due to gravity and
surface tension is important factor for stabilization of the solid-liquid
interface on long length scales. This is a new stabilizing effect different
from the Gibbs-Thomson effect. A particular long wavelength mode of about 1 cm
of wavy pattern observed on the surface of icicles covered with thin layer of
flowing water is obtained from the dispersion relation including the effect of
flow and restoring forces.Comment: 30 pages, 4 figure
Infrared/optical - X-ray simultaneous observations of X-ray flares in GRB 071112C and GRB 080506
We investigate the origin of short X-ray flares which are occasionally
observed in early stages of afterglows of gamma-ray bursts (GRBs). We observed
two events, GRB 071112C and GRB 080506, before the start of X-ray flares in the
optical and near-infrared (NIR) bands with the 1.5-m Kanata telescope. In
conjunction with published X-ray and optical data, we analyzed densely sampled
light curves of the early afterglows and spectral energy distributions (SEDs)
in the NIR-X-ray ranges. We found that the SEDs had a break between the optical
and X-ray bands in the normal decay phases of both GRBs regardless of the model
for the correction of the interstellar extinction in host galaxies of GRBs. In
the X-ray flares, X-ray flux increased by 3 and 15 times in the case of GRB
071112C and 080506, respectively, and the X-ray spectra became harder than
those in the normal decay phases. No significant variation in the optical-NIR
range was detected together with the X-ray flares. These results suggest that
the X-ray flares were associated with either late internal shocks or external
shocks from two-component jets.Comment: 10 pages, 5 figures, accepted to Astronomy and Astrophysic
Complex 2D Matrix Model and Geometrical Map on Complex-Nc Plane
We study the parameter dependence of the internal structure of resonance
states by formulating Complex two-dimensional (2D) Matrix Model, where the two
dimensions represent two-levels of resonances. We calculate a critical value of
the parameter at which "nature transition" with character exchange occurs
between two resonance states, from the viewpoint of geometry on
complex-parameter space. Such critical value is useful to know the internal
structure of resonance states with variation of the parameter in the system. We
apply the model to analyze the internal structure of hadrons with variation of
the color number Nc from infinity to a realistic value 3. By regarding 1/Nc as
the variable parameter in our model, we calculate a critical color number of
nature transition between hadronic states in terms of quark-antiquark pair and
mesonic molecule as exotics from the geometry on complex-Nc plane. For the
large-Nc effective theory, we employ the chiral Lagrangian induced by
holographic QCD with D4/D8/D8-bar multi-D brane system in the type IIA
superstring theory.Comment: 14 pages, 8 figures, 1 table, figures and appendixes added, results
unchange
Decay of Correlations in a Topological Glass
In this paper we continue the study of a topological glassy system. The state
space of the model is given by all triangulations of a sphere with nodes,
half of which are red and half are blue. Red nodes want to have 5 neighbors
while blue ones want 7. Energies of nodes with other numbers of neighbors are
supposed to be positive. The dynamics is that of flipping the diagonal between
two adjacent triangles, with a temperature dependent probability. We consider
the system at very low temperatures.
We concentrate on several new aspects of this model: Starting from a detailed
description of the stationary state, we conclude that pairs of defects (nodes
with the "wrong" degree) move with very high mobility along 1-dimensional
paths. As they wander around, they encounter single defects, which they then
move "sideways" with a geometrically defined probability. This induces a
diffusive motion of the single defects. If they meet, they annihilate, lowering
the energy of the system. We both estimate the decay of energy to equilibrium,
as well as the correlations. In particular, we find a decay like
Hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices
We investigate the hydrodynamic limit for weakly asymmetric simple exclusion
processes in crystal lattices. We construct a suitable scaling limit by using a
discrete harmonic map. As we shall observe, the quasi-linear parabolic equation
in the limit is defined on a flat torus and depends on both the local structure
of the crystal lattice and the discrete harmonic map. We formulate the local
ergodic theorem on the crystal lattice by introducing the notion of local
function bundle, which is a family of local functions on the configuration
space. The ideas and methods are taken from the discrete geometric analysis to
these problems. Results we obtain are extensions of ones by Kipnis, Olla and
Varadhan to crystal lattices.Comment: 41 pages, 7 figure
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