共查询到20条相似文献,搜索用时 125 毫秒
1.
S. A. Guz 《Journal of Experimental and Theoretical Physics》2002,95(1):166-174
A classical Brownian particle is considered in a periodic potential field with a rapidly oscillating phase. The concept of effective potential is used for describing a slow averaged motion of a particle. It is shown that there exists a certain region in which a particle performs a stationary random motion without appreciable drift. By analogy with the ideal case, this region can be called an effective locking region. The situation described is valid for stationary fluctuations of the phase of a potential function, provided that they have a sufficiently small but finite correlation time. The study of the problem is reduced to the analysis of a stochastic system with external noise whose spectral density is zero at zero frequency (“green” noise [1]). The analysis of the first-and second-approximation equations of the averaging method exhibits the high stability of the locking phenomenon. This result has been verified by the numerical solution of appropriate stochastic equations. In this case, a predictor-corrector algorithm was used that allowed one to carry out a numerical simulation to a sufficiently high degree of accuracy. The result of the simulation is in good agreement with the theoretical results. The effective locking bandwidth calculated analytically by the averaging method actually coincides with the value obtained by the simulation. 相似文献
2.
We consider an atomic beam reservoir as a source of quantum noise. The atoms are modelled as two-state systems and interact
one-at-a-time with the system. The Floquet operators are described in terms of the Fermionic creation, annihilation and number
operators associated with the two-state atom. In the limit where the time between interactions goes to zero and the interaction
is suitably scaled, we show that we may obtain a causal (that is, adapted) quantum stochastic differential equation of Hudson—Parthasarathy
type, driven by creation, annihilation and conservation processes. The effect of the Floquet operators in the continuous limit
is exactly captured by the Holevo ordered form for the stochastic evolution 相似文献
3.
Hastings MB 《Physical review letters》2004,93(14):140402
We consider gapped systems governed by either quantum or Markov dynamics, with the low-lying states below the gap being approximately degenerate. For a broad class of dynamics, we prove that ground or stationary state correlation functions can be written as a piece decaying exponentially in space plus a term set by matrix elements between the low-lying states. The key to the proof is a local approximation to the negative energy, or annihilation, part of an operator in a gapped system. Applications to numerical simulation of quantum systems and to networks are discussed. 相似文献
4.
We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk
states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate definition
of the edge conductance may be obtained through a suitable time averaging procedure or by including a contribution from states
in the localized band. In a further result on the Harper Hamiltonian, we show that this contribution is essential. In an appendix
we establish quantized plateaus for the conductance of systems which need not be translation ergodic.
An erratum to this article is available at . 相似文献
5.
In the first part of this paper, we construct an asymptotic expansion for the maximal Lyapunov exponent, the exponential growth rate of solutions to a linear stochastic system, and the rotation numbers for a general four-dimensional dynamical system driven by a small-intensity real noise process. Stability boundaries are obtained provided the natural frequencies are noncommensurable and the infinitesimal generator associated with the noise process has an isolated simple zero eigenvalue. This work is an extension of the work of Sri Namachchivaya and Van Roessel and is general in the sense that general stochastic perturbations of nonautonomous systems with two noncommensurable natural frequencies are considered. 相似文献
6.
M. L. Deng W. Q. Zhu 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(3):391-397
The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation
is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators
under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the
classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic
averaging method. The averaged It? stochastic differential equation describing the energy diffusion and the Pontryagin equation
governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as
the inverse of the MFPT by
solving the Pontryagin equation. The results of two special cases of
broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated
that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation
and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that
the reaction rate can be well predicted using the stochastic averaging method. 相似文献
7.
The coordinate of a white noise driven harmonic oscillator is used as a stochastic source term in bistable dynamics. This new kind of Gaussian colored noise gives rise to resonance phenomena due to a peak in the spectrum. We investigate its effect on linear and bistable systems. We derive a Markovian approximation for driven bistable oscillators and overdamped systems. In the resonance region computer simulations were carried out using an extension of Fox' algorithm procedure for colored noise. We find an increase of the transition rates in bistable systems as compared with the case of bistable systems driven by white and exponentially correlated noise. 相似文献
8.
HAN Yin-Xia LI Jing-Hui CHEN Shi-Gang 《理论物理通讯》2005,44(2):226-230
The phenomenon of stochastic resonance (SR) in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio (SNR) is calculated according to the generalized two-state theory (shown in [H.S. Wio and S. Bouzat, Brazilian J.Phys. 29 (1999) 136]). We find that the SNR increases with the proximity of a to zero. In addition, the correlation time T between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time T between the Gaussian additive colored noise is, the higher of the peak value of SNR. 相似文献
9.
Christoph Gugg Hansjörg Kielhöfer Michael Niggemann 《Communications in Mathematical Physics》2002,230(1):181-199
We prove mathematical approximation results for the (hyperviscous) Burgers equation driven by additive Gaussian noise. In
particular we show that solutions of ``approximating equations' driven by a discretized noise converge towards the solution
of the original equation when the discretization parameter gets small. The convergence takes place in the expected value of
arbitrary powers of certain norms; i.e., all moments of the difference of the solutions tend to zero in certain function spaces.
For the hyperviscous Burgers equation, these results are applied to justify the approximation of certain correlation functions
that play a major role in statistical turbulence theory.
Received: 10 October 2001 / Accepted: 21 May 2002 Published online: 6 August 2002 相似文献
10.
11.
By virtue of the unified-colored-noise approximation the formulas of mean, variance and skewness of first-passage-time distributions (FPTD) for the systems driven by colored noise are derived. The mean and variance of FPTD of bistable system driven by colored noise are calculated. The approximation expressions of the mean, variance and skewness of FPTD for the colored cubic model of a dye laser are obtained. The role of the "color" of pump noise in the dye laser transient is analyzed. 相似文献
12.
Global adaptive synchronization of chaotic systems with uncertain parameters 总被引:3,自引:0,他引:3
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
We propose a novel adaptive synchronization method for a class of nonlinear chaotic systems with uncertain parameters.Using the chaos control method,we derive a synchronizer,which can make the states of the driven system globally track the states of the drive system asymptotically.The advantage of our method is that our problem sctting is more general than those that already exist,and the synchronizer is simply constructed by an analytic formula,without knowledge in advance of the unknown bounds of the uncertain parameters.A computer simulation example is given to validate the proposed approach. 相似文献
13.
Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday. 相似文献
14.
I. Ţifrea M. Crisan I. Grosu 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,79(4):455-464
We consider the transport and the noise characteristic in the case of a triple quantum dots T-shape system where two of the
dots form a two-level system and the other works in a detector-like setup. Our theoretical results are obtained using the
equation of motion method for the case of zero and finite on-site Coulomb interaction in the detector dot. We present analytic
results for the electronic Green’s functions in the system’s component quantum dots, and we used numerical calculations to
evaluate the system’s transport properties. The transport trough the T-shaped system can be controlled by varying the coupling
between the two-level system dots or the coupling between the detector dot and the exterior electrodes. The system’s conductance
presents Fano dips for both strong (fast detector) and weak coupling (slow detector) between the detector dot and the external
electrodes. Due to stronger electronic correlations the noise characteristics in the case of a slow detector are much higher.
This setup may be of interest for the practical realization of qubit states in quantum dots systems. 相似文献
15.
We deal in this paper with systems driven by white or colored Poisson noise. For a free Brownian particle under the influence of white Poisson noise an exact generalized master equation in position space is obtained. In the Gaussian and Smoluchowski limits, known results are recovered. For a general process defined by a stochastic differential equation, with colored Poisson noise, we find an approximate generalized master equation, including first order terms in the correlation time and the first correction to the gaussianity. Under a more restrictive approximation, the stationary distribution function is given. This is used to study the phase transition in the steady state for a Verhulst model. Corrections to the gaussianity are discussed in this case. 相似文献
16.
The motion of a heavy Brownian particle in a low-dimensional bounded solid structure under the effect of a phonon’s excitation
fluctuations is considered. Because of the finiteness of the system, the fluctuation spectrum has zero spectral density at
zero frequency. The effect of this kind of noise, which is conditionally called “green” noise, is studied both analytically
by using the averaging method and numerically on the basis of predictor-corrector algorithms. The effective potential is introduced,
and its form is shown to govern the particle dynamics. Considering a Gaussian potential well (a trap) as an example, it is
demonstrated that green noise leads to abrupt phase transitions in the system as a result of very small parameter variations
(a catastrophe-type effect). The results are compared with the case of white noise in an unbounded structure. From numerical
calculations, it follows that the boundedness of the structure, which changes the noise spectrum, favors a considerable increase
in the lifetime of the particle in the trap. 相似文献
17.
In the present paper, the statistical responses of two-special prey–predator type ecosystem models excited by combined Gaussian and Poisson white noise are investigated by generalizing the stochastic averaging method. First, we unify the deterministic models for the two cases where preys are abundant and the predator population is large, respectively. Then, under some natural assumptions of small perturbations and system parameters, the stochastic models are introduced. The stochastic averaging method is generalized to compute the statistical responses described by stationary probability density functions (PDFs) and moments for population densities in the ecosystems using a perturbation technique. Based on these statistical responses, the effects of ecosystem parameters and the noise parameters on the stationary PDFs and moments are discussed. Additionally, we also calculate the Gaussian approximate solution to illustrate the effectiveness of the perturbation results. The results show that the larger the mean arrival rate, the smaller the difference between the perturbation solution and Gaussian approximation solution. In addition, direct Monte Carlo simulation is performed to validate the above results. 相似文献
18.
We consider the adsorption of an isolated, Gaussian, random, and quenched copolymer chain at an interface. We first propose
a simple analytical method to obtain the adsorption/depletion transition, by averaging over the disorder the partition function
instead of the free energy. The adsorption thresholds obtained by previous authors at a solid/liquid and at a liquid/liquid
interface for multicopolymer chains can be rederived using this method. We also compare the adsorption thresholds obtained
for bimodal and for Gaussian disorder; they only agree for small disorder. We focus on the specific case of an ideally flat
asymmetric liquid/liquid interface, and consider the situation where the chain is composed of monomers of two different chemical
species A and B. The replica method is developed for this case. We show that the Hartree approximation, coupled to a replica symmetry assumption,
leads to the same adsorption thresholds as obtained from our general method. In order to describe the properties of the adsorbed
(or depleted) chain, we develop a new approximation for long chains, within the framework of the replica theory. In most cases,
the behavior of a random copolymer chain can be mapped onto that of a homopolymer chain at an asymmetric attractive interface.
The values of the effective adsorption energy are different for a random and a periodic copolymer chain. Finally, we consider
the case of uncorrelated annealed disorder. The behavior of an annealed chain can be mapped onto that of a homopolymer chain
at an asymmetric non attractive interface; hence, an annealed chain cannot adsorb at an asymmetric interface.
Received 21 January 1999 相似文献
19.
The mean first-passage time (MFPT) and the weak signal detection method of stochastic resonance (SR) on multi-stable nonlinear system under color correlated noise are studied. Using the uniform color noise approximation method, the Fokker-Planck equation of the system is obtained, and the steady-state probability density function of the multi-stable system driven by the multiplicative noise and additive noise is derived. On the basis of this, the formula of MFPT is derived, and the influence of parameters on the MFPT is analyzed. The problem of weak signal detection under color noise background is studied based on multi-stable SR. The results of simulation and experiment show that the method can effectively extract the frequency feature of weak signal in the background of color noise. 相似文献
20.
The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed
to obtain the approximate expressions of MFPT. The effects of non-Gaussian
parameter (measures deviation from Gaussian character) r, the delay
time τ, the noise correlation time
τ0, the intensities D and α of noise on the MFPT are discussed. It is found
that the escape time could be reduced by increasing the delay time τ,
the noise correlation time τ0, or by reducing the
intensities D and α. As far as we know, this is the first time to
consider the effect of delay time on the mean first-passage time in the
stochastic dynamical system. 相似文献