395 research outputs found
Overlap singularity and time evolution in integrable quantum field theory
We study homogeneous quenches in integrable quantum field theory where the
initial state contains zero-momentum particles. We demonstrate that the
two-particle pair amplitude necessarily has a singularity at the two-particle
threshold. Albeit the explicit discussion is carried out for special
(integrable) initial states, we argue that the singularity is inevitably
present and is a generic feature of homogeneous quenches involving the creation
of zero momentum particles. We also identify the singularity in quenches in the
Ising model across the quantum critical point, and compute it perturbatively in
phase quenches in the quantum sine-Gordon model which are potentially relevant
to experiments. We then construct the explicit time dependence of one-point
functions using a linked cluster expansion regulated by a finite volume
parameter. We find that the secular contribution normally linear in time is
modified by a term. We additionally encounter a novel type of secular
contribution which is shown to be related to parametric resonance. It is an
interesting open question to resum the new contributions and to establish their
consequences directly observable in experiments or numerical simulations.Comment: 30+45 pages, 7 figure
Inhomogeneous quantum quenches in the sine-Gordon theory
We study inhomogeneous quantum quenches in the attractive regime of the
sine-Gordon model. In our protocol, the system is prepared in an inhomogeneous
initial state in finite volume by coupling the topological charge density
operator to a Gaussian external field. After switching off the external field,
the subsequent time evolution is governed by the homogeneous sine-Gordon
Hamiltonian. Varying either the interaction strength of the sine-Gordon model
or the amplitude of the external source field, an interesting transition is
observed in the expectation value of the soliton density. This affects both the
initial profile of the density and its time evolution and can be summarised as
a steep transition between behaviours reminiscent of the Klein-Gordon, and the
free massive Dirac fermion theory with initial external fields of high enough
magnitude. The transition in the initial state is also displayed by the
classical sine-Gordon theory and hence can be understood by semi-classical
considerations in terms of the presence of small amplitude field configurations
and the appearance of soliton excitations, which are naturally associated with
bosonic and fermionic excitations on the quantum level, respectively. Features
of the quantum dynamics are also consistent with this correspondence and
comparing them to the classical evolution of the density profile reveals that
quantum effects become markedly pronounced during the time evolution. These
results suggest a crossover between the dominance of bosonic and fermionic
degrees of freedom whose precise identification in terms of the fundamental
particle excitations can be rather non-trivial. Nevertheless, their interplay
is expected to influence the sine-Gordon dynamics in arbitrary inhomogeneous
settings.Comment: 26+18 pages, 12+4 figure
Some results and problems for anisotropic random walks on the plane
This is an expository paper on the asymptotic results concerning path
behaviour of the anisotropic random walk on the two-dimensional square lattice
Z^2. In recent years Mikl\'os and the authors of the present paper investigated
the properties of this random walk concerning strong approximations, local
times and range. We give a survey of these results together with some further
problems.Comment: 20 page
Hysteresis at low Reynolds number: the onset of 2D vortex shedding
Hysteresis has been observed in a study of the transition between laminar
flow and vortex shedding in a quasi-two dimensional system. The system is a
vertical, rapidly flowing soap film which is penetrated by a rod oriented
perpendicular to the film plane. Our experiments show that the transition from
laminar flow to a periodic K\'arm\'an vortex street can be hysteretic, i.e.
vortices can survive at velocities lower than the velocity needed to generate
them.Comment: RevTeX file 4 pages + 5 (encapsulated postscript) figures. to appear
in Phys.Rev.E, Rapid Communicatio
Local Chirality of Low-Lying Dirac Eigenmodes and the Instanton Liquid Model
The reasons for using low-lying Dirac eigenmodes to probe the local structure
of topological charge fluctuations in QCD are discussed, and it is pointed out
that the qualitative double-peaked behavior of the local chiral orientation
probability distribution in these modes is necessary, but not sufficient for
dominance of instanton-like fluctuations. The results with overlap Dirac
operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm
to a~0.12 fm are reported, and it is found that the size and density of local
structures responsible for double-peaking of the distribution are in
disagreement with the assumptions of the Instanton Liquid Model. More
generally, our results suggest that vacuum fluctuations of topological charge
are not effectively dominated by locally quantized (integer-valued) lumps in
QCD.Comment: 29 pages, 13 figures; v2: minor improvements in presentation, results
and conclusions unchanged, version to appear in PR
Theory of Exciton Migration and Field-Induced Dissociation in Conjugated Polymers
The interplay of migration, recombination, and dissociation of excitons in
disordered media is studied theoretically in the low temperature regime. An
exact expression for the photoluminescence spectrum is obtained. The theory is
applied to describe the electric field-induced photoluminescence-quenching
experiments by Kersting et al. [Phys. Rev. Lett. 73, 1440 (1994)] and Deussen
et al. [Synth. Met. 73, 123 (1995)] on conjugated polymer systems. Good
agreement with experiment is obtained using an on-chain dissociation mechanism,
which implies a separation of the electron-hole pair along the polymer chain.Comment: 4 pages, RevTeX, 2 Postscript figure
A study of pentaquarks on the lattice with overlap fermions
We present a quenched lattice QCD calculation of spin-1/2 five-quark states
with quark content for both positive and negative parities. We do
not observe any bound pentaquark state in these channels for either I = 0 or I
=1. The states we found are consistent with KN scattering states which are
checked to exhibit the expected volume dependence of the spectral weight. The
results are based on overlap-fermion propagators on two lattices, 12^3 x 28 and
16^3 x 28, with the same lattice spacing of 0.2 fm, and pion mass as low as ~
180 MeV.Comment: accepted for publication in Phys. Rev.
Chirality Correlation within Dirac Eigenvectors from Domain Wall Fermions
In the dilute instanton gas model of the QCD vacuum, one expects a strong
spatial correlation between chirality and the maxima of the Dirac eigenvectors
with small eigenvalues. Following Horvath, {\it et al.} we examine this
question using lattice gauge theory within the quenched approximation. We
extend the work of those authors by using weaker coupling, , larger
lattices, , and an improved fermion formulation, domain wall fermions. In
contrast with this earlier work, we find a striking correlation between the
magnitude of the chirality density, , and the
normal density, , for the low-lying Dirac eigenvectors.Comment: latex, 25 pages including 12 eps figure
Quantum equivalence of sigma models related by non Abelian Duality Transformations
Coupling constant renormalization is investigated in 2 dimensional sigma
models related by non Abelian duality transformations. In this respect it is
shown that in the one loop order of perturbation theory the duals of a one
parameter family of models, interpolating between the SU(2) principal model and
the O(3) sigma model, exhibit the same behaviour as the original models. For
the O(3) model also the two loop equivalence is investigated, and is found to
be broken just like in the already known example of the principal model.Comment: As a result of the collaboration of new authors the previously
overlooked gauge contribution is inserted into eq.(43) changing not so much
the formulae as part of the conclusion: for the models considered non Abelian
duality is OK in one loo
Reduction of systemic risk by means of Pigouvian taxation
We analyze the possibility of reduction of systemic risk in financial markets through Pigouvian taxation of financial institutions, which is used to support the rescue fund. We introduce the concept of the cascade risk with a clear operational definition as a subclass and a network related measure of the systemic risk. Using financial networks constructed from real Italian money market data and using realistic parameters, we show that the cascade risk can be substantially reduced by a small rate of taxation and by means of a simple strategy of the money transfer from the rescue fund to interbanking market subjects. Furthermore, we show that while negative effects on the return on investment (ROI) are direct and certain, an overall positive effect on risk adjusted return on investments (ROIRA) is visible. Please note that the taxation is introduced as a monetary/regulatory, not as a _scal measure, as the term could suggest. The rescue fund is implemented in a form of a common reserve fund
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