657 research outputs found
Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
We consider a dynamical system described by a system of ordinary differential equations which possesses a compact attracting set Λ of arbitrary shape. Under the assumption of uniform asymptotic stability of Λ in the sense of Lyapunov, we show that discretized versions of the dynamical system involving one-step numerical methods have nearby attracting sets Λ(h), which are also uniformly asymptotically stable. Our proof uses the properties of a Lyapunov function which characterizes the stability of Λ
Measurement-induced two-qubit entanglement in a bad cavity: Fundamental and practical considerations
An entanglement-generating protocol is described for two qubits coupled to a
cavity field in the bad-cavity limit. By measuring the amplitude of a field
transmitted through the cavity, an entangled spin-singlet state can be
established probabilistically. Both fundamental limitations and practical
measurement schemes are discussed, and the influence of dissipative processes
and inhomogeneities in the qubits are analyzed. The measurement-based protocol
provides criteria for selecting states with an infidelity scaling linearly with
the qubit-decoherence rate.Comment: 13 pages, 7 figures, submitted to Phys. Rev.
Stochastic contribution to the growth factor in the LCDM model
We study the effect of noise on the evolution of the growth factor of density
perturbations in the context of the LCDM model. Stochasticity is introduced as
a Wiener process amplified by an intensity parameter alpha. By comparing the
evolution of deterministic and stochastic cases for different values of alpha
we estimate the intensity level necessary to make noise relevant for
cosmological tests based on large-scale structure data. Our results indicate
that the presence of random forces underlying the fluid description can lead to
significant deviations from the nonstochastic solution at late times for
alpha>0.001.Comment: 6 pages, 1 figur
Current-pulse-induced magnetic switching in standard and nonstandard spin-valves
Magnetization switching due to a current-pulse in symmetric and asymmetric
spin valves is studied theoretically within the macrospin model. The switching
process and the corresponding switching parameters are shown to depend
significantly on the pulse duration and also on the interplay of the torques
due to spin transfer and external magnetic field. This interplay leads to
peculiar features in the corresponding phase diagram. These features in
standard spin valves, where the spin transfer torque stabilizes one of the
magnetic configurations (either parallel or antiparallel) and destabilizes the
opposite one, differ from those in nonstandard (asymmetric) spin valves, where
both collinear configurations are stable for one current orientation and
unstable for the opposite one. Following this we propose a scheme of ultrafast
current-induced switching in nonstandard spin valves, based on a sequence of
two current pulses.Comment: 7 pages, 5 figures; to be published in Phys. Rev.
Stochastic memory: memory enhancement due to noise
There are certain classes of resistors, capacitors and inductors that, when
subject to a periodic input of appropriate frequency, develop hysteresis loops
in their characteristic response. Here, we show that the hysteresis of such
memory elements can also be induced by white noise of appropriate intensity
even at very low frequencies of the external driving field. We illustrate this
phenomenon using a physical model of memory resistor realized by
thin films sandwiched between metallic electrodes, and discuss
under which conditions this effect can be observed experimentally. We also
discuss its implications on existing memory systems described in the literature
and the role of colored noise.Comment: 5 pages, 4 figure
Exact corrections for finite-time drift and diffusion coefficients
Real data are constrained to finite sampling rates, which calls for a
suitable mathematical description of the corrections to the finite-time
estimations of the dynamic equations. Often in the literature, lower order
discrete time approximations of the modeling diffusion processes are
considered. On the other hand, there is a lack of simple estimating procedures
based on higher order approximations. For standard diffusion models, that
include additive and multiplicative noise components, we obtain the exact
corrections to the empirical finite-time drift and diffusion coefficients,
based on It\^o-Taylor expansions. These results allow to reconstruct the real
hidden coefficients from the empirical estimates. We also derive higher-order
finite-time expressions for the third and fourth conditional moments, that
furnish extra theoretical checks for that class of diffusive models. The
theoretical predictions are compared with the numerical outcomes of some
representative artificial time-series.Comment: 18 pages, 5 figure
Analysis of stochastic time series in the presence of strong measurement noise
A new approach for the analysis of Langevin-type stochastic processes in the
presence of strong measurement noise is presented. For the case of Gaussian
distributed, exponentially correlated, measurement noise it is possible to
extract the strength and the correlation time of the noise as well as
polynomial approximations of the drift and diffusion functions from the
underlying Langevin equation.Comment: 12 pages, 10 figures; corrected typos and reference
Algebraic structure of stochastic expansions and efficient simulation
We investigate the algebraic structure underlying the stochastic Taylor
solution expansion for stochastic differential systems.Our motivation is to
construct efficient integrators. These are approximations that generate strong
numerical integration schemes that are more accurate than the corresponding
stochastic Taylor approximation, independent of the governing vector fields and
to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is
one example. Herein we: show that the natural context to study stochastic
integrators and their properties is the convolution shuffle algebra of
endomorphisms; establish a new whole class of efficient integrators; and then
prove that, within this class, the sinhlog integrator generates the optimal
efficient stochastic integrator at all orders.Comment: 19 page
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