720 research outputs found
Theory of Second and Higher Order Stochastic Processes
This paper presents a general approach to linear stochastic processes driven
by various random noises. Mathematically, such processes are described by
linear stochastic differential equations of arbitrary order (the simplest
non-trivial example is , where is not a Gaussian white
noise). The stochastic process is discretized into time-steps, all possible
realizations are summed up and the continuum limit is taken. This procedure
often yields closed form formulas for the joint probability distributions.
Completely worked out examples include all Gaussian random forces and a large
class of Markovian (non-Gaussian) forces. This approach is also useful for
deriving Fokker-Planck equations for the probability distribution functions.
This is worked out for Gaussian noises and for the Markovian dichotomous noise.Comment: 35 pages, PlainTex, accepted for publication in Phys Rev. E
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
Rectifying fluctuations in an optical lattice
We have realized a Brownian motor by using cold atoms in a dissipative
optical lattice as a model system. In our experiment the optical potential is
spatially symmetric and the time-symmetry of the system is broken by applying
appropriate zero-mean ac forces. We identify a regime of rectification of
forces and a regime of rectification of fluctuations, the latter corresponding
to the realization of a Brownian motor
A phase transition in a system driven by coloured noise
For a system driven by coloured noise, we investigate the activation energy of escape, and the dynamics during the escape. We have performed analogue experiments to measure the change in activation energy as the power spectrum of the noise varies. An adiabatic approach based on path integral theory allows us to calculate analytically the critical value at which a phase transition in the activation energy occurs
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
Scalable design of tailored soft pulses for coherent control
We present a scalable scheme to design optimized soft pulses and pulse
sequences for coherent control of interacting quantum many-body systems. The
scheme is based on the cluster expansion and the time dependent perturbation
theory implemented numerically. This approach offers a dramatic advantage in
numerical efficiency, and it is also more convenient than the commonly used
Magnus expansion, especially when dealing with higher order terms. We
illustrate the scheme by designing 2nd-order pi-pulses and a 6th-order 8-pulse
refocusing sequence for a chain of qubits with nearest-neighbor couplings. We
also discuss the performance of soft-pulse refocusing sequences in suppressing
decoherence due to low-frequency environment.Comment: 4 pages, 2 tables. (modified first table, references added, minor
text changes
Supernarrow spectral peaks near a kinetic phase transition in a driven, nonlinear micromechanical oscillator
We measure the spectral densities of fluctuations of an underdamped nonlinear
micromechanical oscillator. By applying a sufficiently large periodic
excitation, two stable dynamical states are obtained within a particular range
of driving frequency. White noise is injected into the excitation, allowing the
system to overcome the activation barrier and switch between the two states.
While the oscillator predominately resides in one of the two states for most
excitation frequencies, a narrow range of frequencies exist where the
occupations of the two states are approximately equal. At these frequencies,
the oscillator undergoes a kinetic phase transition that resembles the phase
transition of thermal equilibrium systems. We observe a supernarrow peak in the
power spectral densities of fluctuations of the oscillator. This peak is
centered at the excitation frequency and arises as a result of noise-induced
transitions between the two dynamical states.Comment: 4 pages, 4 figure
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
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