914 research outputs found
Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
The master equation describing non-equilibrium one-dimensional problems like
diffusion limited reactions or critical dynamics of classical spin systems can
be written as a Schr\"odinger equation in which the wave function is the
probability distribution and the Hamiltonian is that of a quantum chain with
nearest neighbor interactions. Since many one-dimensional quantum chains are
integrable, this opens a new field of applications. At the same time physical
intuition and probabilistic methods bring new insight into the understanding of
the properties of quantum chains. A simple example is the asymmetric diffusion
of several species of particles which leads naturally to Hecke algebras and
-deformed quantum groups. Many other examples are given. Several relevant
technical aspects like critical exponents, correlation functions and
finite-size scaling are also discussed in detail.Comment: Latex 52 pages (2 figures appended at the end), UGVA-DPT 1992/12-79
On the universality of a class of annihilation-coagulation models
A class of -dimensional reaction-diffusion models interpolating
continuously between the diffusion-coagulation and the diffusion-annihilation
models is introduced. Exact relations among the observables of different models
are established. For the one-dimensional case, it is shown how correlations in
the initial state can lead to non-universal amplitudes for time-dependent
particles density.Comment: 18 pages with no figures. Latex file using REVTE
Temperature in nonequilibrium systems with conserved energy
We study a class of nonequilibrium lattice models which describe local
redistributions of a globally conserved energy. A particular subclass can be
solved analytically, allowing to define a temperature T_{th} along the same
lines as in the equilibrium microcanonical ensemble. The
fluctuation-dissipation relation is explicitely found to be linear, but its
slope differs from the inverse temperature T_{th}^{-1}. A numerical
renormalization group procedure suggests that, at a coarse-grained level, all
models behave similarly, leading to a two-parameter description of their
macroscopic properties.Comment: 4 pages, 1 figure, final versio
Can the post-Newtonian gravitational waveform of an inspiraling binary be improved by solving the energy balance equation numerically?
The detection of gravitational waves from inspiraling compact binaries using
matched filtering depends crucially on the availability of accurate template
waveforms. We determine whether the accuracy of the templates' phasing can be
improved by solving the post-Newtonian energy balance equation numerically,
rather than (as is normally done) analytically within the post-Newtonian
perturbative expansion. By specializing to the limit of a small mass ratio, we
find evidence that there is no gain in accuracy.Comment: 13 pages, RevTeX, 5 figures included via eps
Dynamical real-space renormalization group calculations with a new clustering scheme on random networks
We have defined a new type of clustering scheme preserving the connectivity
of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving
process. Our new clustering scheme performs much better for correlation length
and dynamical critical exponents in high dimensions, where the conventional
Migdal-Kadanoff bond moving scheme breaks down. In two and three dimensions we
find the dynamical critical exponents for the kinetic Ising Model to be z=2.13
and z=2.09, respectively at pure Ising fixed point. These values are in very
good agreement with recent Monte Carlo results. We investigate the phase
diagram and the critical behaviour for randomly bond diluted lattices in d=2
and 3, in the light of this new transformation. We also provide exact
correlation exponent and dynamical critical exponent values on hierarchical
lattices with power-law degree distributions, both in the pure and random
cases.Comment: 8 figure
Dynamical phase transition in one-dimensional kinetic Ising model with nonuniform coupling constants
An extension of the Kinetic Ising model with nonuniform coupling constants on
a one-dimensional lattice with boundaries is investigated, and the relaxation
of such a system towards its equilibrium is studied. Using a transfer matrix
method, it is shown that there are cases where the system exhibits a dynamical
phase transition. There may be two phases, the fast phase and the slow phase.
For some region of the parameter space, the relaxation time is independent of
the reaction rates at the boundaries. Changing continuously the reaction rates
at the boundaries, however, there is a point where the relaxation times begins
changing, as a continuous (nonconstant) function of the reaction rates at the
boundaries, so that at this point there is a jump in the derivative of the
relaxation time with respect to the reaction rates at the boundaries.Comment: 17 page
A field theoretic approach to master equations and a variational method beyond the Poisson ansatz
We develop a variational scheme in a field theoretic approach to a stochastic
process. While various stochastic processes can be expressed using master
equations, in general it is difficult to solve the master equations exactly,
and it is also hard to solve the master equations numerically because of the
curse of dimensionality. The field theoretic approach has been used in order to
study such complicated master equations, and the variational scheme achieves
tremendous reduction in the dimensionality of master equations. For the
variational method, only the Poisson ansatz has been used, in which one
restricts the variational function to a Poisson distribution. Hence, one has
dealt with only restricted fluctuation effects. We develop the variational
method further, which enables us to treat an arbitrary variational function. It
is shown that the variational scheme developed gives a quantitatively good
approximation for master equations which describe a stochastic gene regulatory
network.Comment: 13 pages, 2 figure
Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
Considering a gas of self-propelled particles with binary interactions, we
derive the hydrodynamic equations governing the density and velocity fields
from the microscopic dynamics, in the framework of the associated Boltzmann
equation. Explicit expressions for the transport coefficients are given, as a
function of the microscopic parameters of the model. We show that the
homogeneous state with zero hydrodynamic velocity is unstable above a critical
density (which depends on the microscopic parameters), signaling the onset of a
collective motion. Comparison with numerical simulations on a standard model of
self-propelled particles shows that the phase diagram we obtain is robust, in
the sense that it depends only slightly on the precise definition of the model.
While the homogeneous flow is found to be stable far from the transition line,
it becomes unstable with respect to finite-wavelength perturbations close to
the transition, implying a non trivial spatio-temporal structure for the
resulting flow. We find solitary wave solutions of the hydrodynamic equations,
quite similar to the stripes reported in direct numerical simulations of
self-propelled particles.Comment: 33 pages, 11 figures, submitted to J. Phys.
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