480 research outputs found
Universality in escape from a modulated potential well
We show that the rate of activated escape from a periodically modulated
potential displays scaling behavior versus modulation amplitude . For
adiabatic modulation of an optically trapped Brownian particle, measurements
yield with . The theory gives
in the adiabatic limit and predicts a crossover to scaling as
approaches the bifurcation point where the metastable state disappears.Comment: 4 pages, 3 figure
Large rare fluctuations in systems with delayed dissipation
We study the probability distribution and the escape rate in systems with
delayed dissipation that comes from the coupling to a thermal bath. To
logarithmic accuracy in the fluctuation intensity, the problem is reduced to a
variational problem. It describes the most probable fluctuational paths, which
are given by acausal equations due to the delay. In thermal equilibrium, the
most probable path passing through a remote state has time reversal symmetry,
even though one cannot uniquely define a path that starts from a state with
given system coordinate and momentum. The corrections to the distribution and
the escape activation energy for small delay and small noise correlation time
are obtained in the explicit form.Comment: 9 page
Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator
We study noise-enhanced frequency mixing in an underdamped micromechanical
torsional oscillator. The oscillator is electrostatically driven into
bistability by a strong, periodic voltage at frequency . A second,
weak ac voltage is applied at a frequency close to . Due to
nonlinearity in the system, vibrations occur at both and
. White noise is injected into the excitation, allowing the
system to occasionally overcome the activation barrier and switch between the
two states. At the primary drive frequency where the occupations of the two
states are approximately equal, we observe noise-induced enhancement of the
oscillation amplitudes at both and the down-converted frequency
, in agreement with theoretical predictions. Such enhancement
occurs as a result of the noise-induced interstate transitions becoming
synchronous with the beating between the two driving frequencies.Comment: 4 pages 5 figure
Scaling and crossovers in activated escape near a bifurcation point
Near a bifurcation point a system experiences critical slowing down. This
leads to scaling behavior of fluctuations. We find that a periodically driven
system may display three scaling regimes and scaling crossovers near a
saddle-node bifurcation where a metastable state disappears. The rate of
activated escape scales with the driving field amplitude as , where is the bifurcational value of . With
increasing field frequency the critical exponent changes from
for stationary systems to a dynamical value and then again to
. The analytical results are in agreement with the results of
asymptotic calculations in the scaling region. Numerical calculations and
simulations for a model system support the theory.Comment: 18 page
Effects of noise on hysteresis and resonance width in graphene and nanotubes resonators
We investigate the role that noise plays in the hysteretic dynamics of a
suspended nanotube or a graphene sheet subject to an oscillating force. We find
that not only the size but also the position of the hysteresis region in these
systems can be controlled by noise. We also find that nano-resonators act as
noise rectifiers: by increasing the noise in the setup, the resonance width of
the characteristic peak in these systems is reduced and, as a result, the
quality factor is increased.Comment: 15 pages, 6 figures. Sent to PRB (in revision
Magneto-shear modes and a.c. dissipation in a two-dimensional Wigner crystal
The a.c. response of an unpinned and finite 2D Wigner crystal to electric
fields at an angular frequency has been calculated in the dissipative
limit, , where is the scattering rate. For
electrons screened by parallel electrodes, in zero magnetic field the
long-wavelength excitations are a diffusive longitudinal transmission line mode
and a diffusive shear mode. A magnetic field couples these modes together to
form two new magneto-shear modes. The dimensionless coupling parameter where and are the
speeds of transverse and longitudinal sound in the collisionless limit and
and are the tensor components of the
magnetoconductivity. For , both the coupled modes contribute
to the response of 2D electrons in a Corbino disk measurement of
magnetoconductivity. For , the electron crystal rotates rigidly in
a magnetic field. In general, both the amplitude and phase of the measured a.c.
currents are changed by the shear modulus. In principle, both the
magnetoconductivity and the shear modulus can be measured simultaneously.Comment: REVTeX, 7 pp., 4 eps figure
RF bifurcation of a Josephson junction: microwave embedding circuit requirements
A Josephson tunnel junction which is RF-driven near a dynamical bifurcation
point can amplify quantum signals. The bifurcation point will exist robustly
only if the electrodynamic environment of the junction meets certain criteria.
In this article we develop a general formalism for dealing with the non-linear
dynamics of Josephson junction embedded in an arbitrary microwave circuit. We
find sufficient conditions for the existence of the bifurcation regime: a) the
embedding impedance of the junction need to present a resonance at a particular
frequency , with the quality factor of the resonance and the
participation ratio of the junction satisfying , b) the drive
frequency should be low frequency detuned away from by more than
.Comment: Submitted to Phys. Rev. B, 12 pages, 6 figure
Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
The extinction of a single species due to demographic stochasticity is
analyzed. The discrete nature of the individual agents and the Poissonian noise
related to the birth-death processes result in local extinction of a metastable
population, as the system hits the absorbing state. The Fokker-Planck
formulation of that problem fails to capture the statistics of large deviations
from the metastable state, while approximations appropriate close to the
absorbing state become, in general, invalid as the population becomes large. To
connect these two regimes, a master equation based on a real space WKB method
is presented, and is shown to yield an excellent approximation for the decay
rate and the extreme events statistics all the way down to the absorbing state.
The details of the underlying microscopic process, smeared out in a mean field
treatment, are shown to be crucial for an exact determination of the extinction
exponent. This general scheme is shown to reproduce the known results in the
field, to yield new corollaries and to fit quite precisely the numerical
solutions. Moreover it allows for systematic improvement via a series expansion
where the small parameter is the inverse of the number of individuals in the
metastable state
Thermal Resonance in Signal Transmission
We use temperature tuning to control signal propagation in simple
one-dimensional arrays of masses connected by hard anharmonic springs and with
no local potentials. In our numerical model a sustained signal is applied at
one site of a chain immersed in a thermal environment and the signal-to-noise
ratio is measured at each oscillator. We show that raising the temperature can
lead to enhanced signal propagation along the chain, resulting in thermal
resonance effects akin to the resonance observed in arrays of bistable systems.Comment: To appear in Phys. Rev.
Detecting and characterizing frequency fluctuations of vibrational modes
We show how frequency fluctuations of a vibrational mode can be separated
from other sources of phase noise. The method is based on the analysis of the
time dependence of the complex amplitude of forced vibrations. The moments of
the complex amplitude sensitively depend on the frequency noise statistics and
its power spectrum. The analysis applies to classical and to quantum
vibrations
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