61 research outputs found
Non-Hermitian Delocalization and Eigenfunctions
Recent literature on delocalization in non-Hermitian systems has stressed
criteria based on sensitivity of eigenvalues to boundary conditions and the
existence of a non-zero current. We emphasize here that delocalization also
shows up clearly in eigenfunctions, provided one studies the product of left-
and right-eigenfunctions, as required on physical grounds, and not simply the
squared modulii of the eigenfunctions themselves. We also discuss the right-
and left-eigenfunctions of the ground state in the delocalized regime and
suggest that the behavior of these functions, when considered separately, may
be viewed as ``intermediate'' between localized and delocalized.Comment: 8 pages, 11 figures include
Solution of an infection model near threshold
We study the Susceptible-Infected-Recovered model of epidemics in the
vicinity of the threshold infectivity. We derive the distribution of total
outbreak size in the limit of large population size . This is accomplished
by mapping the problem to the first passage time of a random walker subject to
a drift that increases linearly with time. We recover the scaling results of
Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales
as , with the average scaling as , with an explicit form for
the scaling function
Finite Size Effects in Vortex Localization
The equilibrium properties of flux lines pinned by columnar disorder are
studied, using the analogy with the time evolution of a diffusing scalar
density in a randomly amplifying medium. Near H_{c1}, the physical features of
the vortices in the localized phase are shown to be determined by the density
of states near the band edge. As a result, H_{c1} is inversely proportional to
the logarithm of the sample size, and the screening length of the perpendicular
magnetic field decreases with temperature. For large tilt the extended ground
state turns out to wander in the plane perpendicular to the defects with
exponents corresponding to a directed polymer in a random medium, and the
energy difference between two competing metastable states in this case is
extensive. The divergence of the effective potential associated with strong
pinning centers as the tilt approaches its critical value is discussed as well.Comment: 10 pages, 2 figure
Directed percolation with a single defect site
In a recent study [arXiv:1011.3254] the contact process with a modified
creation rate at a single site was shown to exhibit a non-universal scaling
behavior with exponents varying with the creation rate at the special site. In
the present work we argue that the survival probability decays according to a
stretched exponential rather than a power law, explaining previous
observations.Comment: 8 pages, 3 figure
Transition Phenomena Induced by Internal Noise and Quasi-absorbing State
We study a simple chemical reaction system and effects of the internal noise.
The chemical reaction system causes the same transition phenomenon discussed by
Togashi and Kaneko [Phys. Rev. Lett. 86 (2001) 2459; J. Phys. Soc. Jpn. 72
(2003) 62]. By using the simpler model than Togashi-Kaneko's one, we discuss
the transition phenomenon by means of a random walk model and an effective
model. The discussion makes it clear that quasi-absorbing states, which are
produced by the change of the strength of the internal noise, play an important
role in the transition phenomenon. Stabilizing the quasi-absorbing states
causes bifurcation of the peaks in the stationary probability distribution
discontinuously.Comment: 6 pages, 5 figure
Inverse Symmetry Breaking in Multi-Scalar Field Theories
We review how the phenomena of inverse symmetry breaking (and symmetry
nonrestoration) may arise in the context of relativistic as well as
nonrelativistic multi-scalar field theories. We discuss how the consideration
of thermal effects on the couplings produce different transition patterns for
both theories. For the relativistic case, these effects allow the appearance of
inverse symmetry breaking (and symmetry nonrestoration) at arbitrarily large
temperatures. On the other hand, the same phenomena are suppressed in the
nonrelativistic case, which is relevant for condensed matter physics. In this
case, symmetry nonrestoration does not happen while inverse symmetry is allowed
only to be followed by symmetry restoration characterizing a reentrant phase.
The aim of this paper is to give more insight concerning the, qualitatively
correct, results obtained by using one loop perturbation theory in the
evaluation of thermal masses and couplings.Comment: 7 pages, 3 figures, talk given at the workshop on Quantum Fields
Under the Influence of External Conditions, QFEXT05, Barcelona, sep-200
Symmetry Aspects in Nonrelativistic Multi-Scalar Field Models and Application to a Coupled Two-Species Dilute Bose Gas
We discuss unusual aspects of symmetry that can happen due to entropic
effects in the context of multi-scalar field theories at finite temperature. We
present their consequences, in special, for the case of nonrelativistic models
of hard core spheres. We show that for nonrelativistic models phenomena like
inverse symmetry breaking and symmetry non-restoration cannot take place, but a
reentrant phase at high temperatures is shown to be possible for some region of
parameters. We then develop a model of interest in studies of Bose-Einstein
condensation in dilute atomic gases and discuss about its phase transition
patterns. In this application to a Bose-Einstein condensation model, however,
no reentrant phases are found.Comment: 8 pages, 1 eps figure, IOP style. Based on a talk given by R. O.
Ramos at the QFEXT05 workshop, Barcelona, Spain, September 5-9, 2005. One
reference was update
Monte Carlo simulation of the transmission of measles: Beyond the mass action principle
We present a Monte Carlo simulation of the transmission of measles within a
population sample during its growing and equilibrium states by introducing two
different vaccination schedules of one and two doses. We study the effects of
the contact rate per unit time as well as the initial conditions on the
persistence of the disease. We found a weak effect of the initial conditions
while the disease persists when lies in the range 1/L-10/L ( being
the latent period). Further comparison with existing data, prediction of future
epidemics and other estimations of the vaccination efficiency are provided.
Finally, we compare our approach to the models using the mass action
principle in the first and another epidemic region and found the incidence
independent of the number of susceptibles after the epidemic peak while it
strongly fluctuates in its growing region. This method can be easily applied to
other human, animals and vegetable diseases and includes more complicated
parameters.Comment: 15 pages, 4 figures, 1 table, Submitted to Phys.Rev.
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