539 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
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
Proposal for manipulating and detecting spin and orbital states of trapped electrons on helium using cavity quantum electrodynamics
We propose to couple an on-chip high finesse superconducting cavity to the
lateral-motion and spin state of a single electron trapped on the surface of
superfluid helium. We estimate the motional coherence times to exceed 15
microseconds, while energy will be coherently exchanged with the cavity photons
in less than 10 nanoseconds for charge states and faster than 1 microsecond for
spin states, making the system attractive for quantum information processing
and cavity quantum electrodynamics experiments. Strong interaction with cavity
photons will provide the means for both nondestructive readout and coupling of
distant electrons.Comment: 4 pages, 3 figures, supplemental material
Lifetime of metastable states in resonant tunneling structures
We investigate the transport of electrons through a double-barrier
resonant-tunneling structure in the regime where the current-voltage
characteristics exhibit bistability. In this regime one of the states is
metastable, and the system eventually switches from it to the stable state. We
show that the mean switching time grows exponentially as the voltage across the
device is tuned from the its boundary value into the bistable region. In
samples of small area we find that the logarithm of the lifetime is
proportional to the voltage (measured from its boundary value) to the 3/2
power, while in larger samples the logarithm of the lifetime is linearly
proportional to the voltage.Comment: REVTeX 4, 5 pages, 3 EPS-figure
Poisson-noise induced escape from a metastable state
We provide a complete solution of the problems of the probability
distribution and the escape rate in Poisson-noise driven systems. It includes
both the exponents and the prefactors. The analysis refers to an overdamped
particle in a potential well. The results apply for an arbitrary average rate
of noise pulses, from slow pulse rates, where the noise acts on the system as
strongly non-Gaussian, to high pulse rates, where the noise acts as effectively
Gaussian
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
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
Noise-enabled precision measurements of a Duffing nanomechanical resonator
We report quantitative experimental measurements of the nonlinear response of
a radiofrequency mechanical resonator, with very high quality factor, driven by
a large swept-frequency force. We directly measure the noise-free transition
dynamics between the two basins of attraction that appear in the nonlinear
regime, and find good agreement with those predicted by the one-dimensional
Duffing equation of motion. We then measure the response of the transition
rates to controlled levels of white noise, and extract the activation energy
from each basin. The measurements of the noise-induced transitions allow us to
obtain precise values for the critical frequencies, the natural resonance
frequency, and the cubic nonlinear parameter in the Duffing oscillator, with
direct applications to high sensitivity parametric sensors based on these
resonators.Comment: 5 pages, 5 figure
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