597 research outputs found
Diffusion-induced bistability of driven nanomechanical resonators
We study nanomechanical resonators with frequency fluctuations due to
diffusion of absorbed particles. The diffusion depends on the vibration
amplitude through inertial effect. We find that, if the diffusion coefficient
is sufficiently large, the resonator response to periodic driving displays
bistability. The lifetime of the coexisting vibrational states scales
exponentially with the diffusion coefficient. It also displays a characteristic
scaling dependence on the distance to bifurcation points.Comment: 4 pages, 3 figure
Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
We study a large population of globally coupled phase oscillators subject to
common white Gaussian noise and find analytically that the critical coupling
strength between oscillators for synchronization transition decreases with an
increase in the intensity of common noise. Thus, common noise promotes the
onset of synchronization. Our prediction is confirmed by numerical simulations
of the phase oscillators as well as of limit-cycle oscillators
Multiplicative Noise: Applications in Cosmology and Field Theory
Physical situations involving multiplicative noise arise generically in
cosmology and field theory. In this paper, the focus is first on exact
nonlinear Langevin equations, appropriate in a cosmologica setting, for a
system with one degree of freedom. The Langevin equations are derived using an
appropriate time-dependent generalization of a model due to Zwanzig. These
models are then extended to field theories and the generation of multiplicative
noise in such a context is discussed. Important issues in both the cosmological
and field theoretic cases are the fluctuation-dissipation relations and the
relaxation time scale. Of some importance in cosmology is the fact that
multiplicative noise can substantially reduce the relaxation time. In the field
theoretic context such a noise can lead to a significant enhancement in the
nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210
Quantum State Diffusion and Time Correlation Functions
In computing the spectra of quantum mechanical systems one encounters the
Fourier transforms of time correlation functions, as given by the quantum
regression theorem for systems described by master equations. Quantum state
diffusion (QSD) gives a useful method of solving these problems by unraveling
the master equation into stochastic trajectories; but there is no generally
accepted definition of a time correlation function for a single QSD trajectory.
In this paper we show how QSD can be used to calculate these spectra directly;
by formally solving the equations which arise, we arrive at a natural
definition for a two-time correlation function in QSD, which depends explicitly
on both the stochastic noise of the particular trajectory and the time of
measurement, and which agrees in the mean with the ensemble average definition
of correlation functions.Comment: 16 pages standard LaTeX + 1 figure (uuencoded postscript) Numerous
minor revisions and clarifications. To appear in J. Mod. Optic
Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources
We study the statistical properties of overdamped particles driven by two
cross-correlated multiplicative Gaussian white noises in a time-dependent
environment. Using the Langevin and Fokker-Planck approaches, we derive the
exact probability distribution function for the particle positions, calculate
its moments and find their corresponding long-time, asymptotic behaviors. The
generally anomalous diffusive regimes of the particles are classified, and
their dependence on the friction coefficient and the characteristics of the
noises is analyzed in detail. The asymptotic predictions are confirmed by exact
solutions for two examples.Comment: 15 page
Discreteness-induced Transition in Catalytic Reaction Networks
Drastic change in dynamics and statistics in a chemical reaction system,
induced by smallness in the molecule number, is reported. Through stochastic
simulations for random catalytic reaction networks, transition to a novel state
is observed with the decrease in the total molecule number N, characterized by:
i) large fluctuations in chemical concentrations as a result of intermittent
switching over several states with extinction of some molecule species and ii)
strong deviation of time averaged distribution of chemical concentrations from
that expected in the continuum limit, i.e., . The origin of
transition is explained by the deficiency of molecule leading to termination of
some reactions. The critical number of molecules for the transition is obtained
as a function of the number of molecules species M and that of reaction paths
K, while total reaction rates, scaled properly, are shown to follow a universal
form as a function of NK/M
Three-photon states in nonlinear crystal superlattices
It has been a longstanding goal in quantum optics to realize controllable
sources generating joint multiphoton states, particularly, photon triplet with
arbitrary spectral characteristics. We demonstrate that such sources can be
realized via cascaded parametric down-conversion (PDC) in superlattice
structures of nonlinear and linear segments. We consider scheme that involves
two parametric processes: ,
under pulsed pump and investigate
spontaneous creation of photon triplet as well as generation of high-intensity
mode in intracavity three-photon splitting. We show preparation of
Greenberger-Horne-Zeilinger polarization entangled states in cascaded type-II
and type-I PDC in framework of consideration dual-grid structure that involves
two periodically-poled crystals. We demonstrate the method of compensation of
the dispersive effects in non-linear segments by appropriately chosen linear
dispersive segments of superlattice for preparation heralded joint states of
two polarized photons. In the case of intracavity three-photon splitting, we
concentrate on investigation of photon-number distributions, third-order
photon-number correlation function as well as the Wigner functions. These
quantities are observed both for short interaction time intervals and in over
transient regime, when dissipative effects are essential.Comment: 15 pages, 6 figure
Universal shape law of stochastic supercritical bifurcations: Theory and experiments
A universal law for the supercritical bifurcation shape of transverse
one-dimensional (1D) systems in presence of additive noise is given. The
stochastic Langevin equation of such systems is solved by using a Fokker-Planck
equation leading to the expression for the most probable amplitude of the
critical mode. From this universal expression, the shape of the bifurcation,
its location and its evolution with the noise level are completely defined.
Experimental results obtained for a 1D transverse Kerr-like slice subjected to
optical feedback are in excellent agreement.Comment: 5 pages, 5 figure
Switching Dynamics in Reaction Networks Induced by Molecular Discreteness
To study the fluctuations and dynamics in chemical reaction processes,
stochastic differential equations based on the rate equation involving chemical
concentrations are often adopted. When the number of molecules is very small,
however, the discreteness in the number of molecules cannot be neglected since
the number of molecules must be an integer. This discreteness can be important
in biochemical reactions, where the total number of molecules is not
significantly larger than the number of chemical species. To elucidate the
effects of such discreteness, we study autocatalytic reaction systems
comprising several chemical species through stochastic particle simulations.
The generation of novel states is observed; it is caused by the extinction of
some molecular species due to the discreteness in their number. We demonstrate
that the reaction dynamics are switched by a single molecule, which leads to
the reconstruction of the acting network structure. We also show the strong
dependence of the chemical concentrations on the system size, which is caused
by transitions to discreteness-induced novel states.Comment: 11 pages, 5 figure
Macroscopic description of particle systems with non-local density-dependent diffusivity
In this paper we study macroscopic density equations in which the diffusion
coefficient depends on a weighted spatial average of the density itself. We
show that large differences (not present in the local density-dependence case)
appear between the density equations that are derived from different
representations of the Langevin equation describing a system of interacting
Brownian particles. Linear stability analysis demonstrates that under some
circumstances the density equation interpreted like Ito has pattern solutions,
which never appear for the Hanggi-Klimontovich interpretation, which is the
other one typically appearing in the context of nonlinear diffusion processes.
We also introduce a discrete-time microscopic model of particles that confirms
the results obtained at the macroscopic density level.Comment: 4 pages, 3 figure
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