Ornstein-Uhlenbeck Noise Research Articles

A class of solvable nonlinear Langevin equation driven by multiplicative colored noise

A solution is obtained from a wide class of the nonlinear Langevin equation driven by the multiplicative Ornstein–Uhlenbeck noise, with the drift and diffusion coefficients separable in time and space. It is possible to demonstrate that the probability distribution function recovers the result of the system driven by the Gaussian white noise. The solution unifies various previous results presented in the literature. The technique can also be used for investigating the system driven by other colored noises.

Frozen entanglement and quantum correlations of one-parameter qubit−qutrit states under classical noise effects

We provide a detailed analysis of the dynamics of entanglement and quantum correlations for one-parameter qubit-qutrit states under independent or common classical noises influence. Namely the static noise, the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise. Independently of the intrinsic features of the noises, entanglement measured by negativity and quantum correlations measured by measured-induced disturbance (MID) vanish after a finite time under the effects of independent noise environments. In a common environment setup, we show the existence of specific and very important features of perfect insulation of the systems quantum properties from noise effects, for suitable range of the entanglement parameter. We refer these phenomena to as frozen entanglement and frozen quantum correlations. The dichotomy between entanglement (separability) and quantum correlations is strengthened by our results, with the robustness of MID over entanglement and existence of separable qubit-qutrit states with non-zero quantum correlations.

Energetics of single-well undamped stochastic oscillators.

This paper discusses analytical and numerical results for nonharmonic, undamped, single-well, stochastic oscillators driven by additive noises. It focuses on average kinetic, potential, and total energies together with the corresponding distributions under random drivings, involving Gaussian white, Ornstein-Uhlenbeck, and Markovian dichotomous noises. It demonstrates that insensitivity of the average total energy to the single-well potential type, V(x)∝x^{2n}, under Gaussian white noise does not extend to other noise types. Nevertheless, in the long-time limit (t→∞), the average energies grow as power law with exponents dependent on the steepness of the potential n. Another special limit corresponds to n→∞, i.e., to the infinite rectangular potential well, when the average total energy grows as a power law with the same exponent for all considered noise types.

The dynamics of tripartite quantum correlations under Ornstein–Uhlenbeck noise

The dynamics of the tripartite thermal entanglement measured by Negativity (N) and the tripartite quantum correlation described by measurement-induced disturbance (MID) under Ornstein–Uhlenbeck noise are investigated. This study has found that the tripartite N and MID can be preserved more effectively in the non-Markovian environment than in the short-time limit and the Markov limit cases. The short-time limit is a better approximation than the Markov limit. MID vanishes only in the asymptotic limit, while entanglement sudden death may occur, and the decreasing duration of MID far outweighs entanglement. This implies that MID is more robust than Negativity. As the noise bandwidth increases, the disentanglement time and the decay time of MID are significantly shorter. The increase of XZX[Formula: see text]+[Formula: see text]YZY three-site interaction is more effective than XZY−YZX three-site interaction to enhance Negativity and MID as well as the disentanglement time. The magnetic field diminishes Negativity and MID, but has no significant influence on the decreasing durations of both Negativity and MID.

Decoherence and protection of entanglement of a system of three qubits driven by a classical Gaussian distributed fluctuating field

We consider a system of three uncoupled entangled qubits undergoing a decoherence process (DP) induced by a classical environmental noise portrayed by a Gaussian distributed fluctuating field with either Ornstein–Uhlenbeck (OU) or Gaussian (G) autocorrelation function. The impacts of such a DP on the entanglement of the qubits are analyzed in detail when they are initialized either in the GHZ- or W-type states and interact with the fluctuating field in three different scenarios namely, common, independent and mixed environment(s). We found that: (i) the way the qubits interact with the noise as well as their initial state play an important role towards the protection of entanglement; (ii) there are optimal parameters which permit to delay or totally avoid the disentanglement of the qubits; (iii) irrespective of the qubit-noise coupling (QNC) scenario and the initial prepared state considered, the OU noise is more injurious to the survivorship of entanglement than the G one. Specifically, we show that, irrespective of the QNC scenario and the character of the noise considered, the DP disentangles the qubits more quickly when they are initialized in the W-type states than in the GHZ-type one. Furthermore, we show that when the initial state of the qubits is considered to be a W-type state, the disentanglement occurs more rapidly in the common environment (CE) scenario followed by the mixed environments (MEs) scenario than in the independent environments (IEs) one. However, the situation is completely reversed when a GHZ-type state is considered.

When underwater degraded images meet logical stochastic resonance

Owing to light attenuation and high background noise, underwater images are significantly degraded, which hiders the development of underwater exploration. However, noise itself can be used to counter noise. In this paper, we apply logical stochastic resonance (LSR) to help detect weak objects from low-quality underwater images. On the basis of analysis of the physical character of underwater images, three models, namely basic dynamical system driven by Gaussian noise, basic dynamical system driven by Ornstein–Uhlenbeck (OU) noise, and dynamical system with extra delay loop, are chosen to study the performance of LSR-based object detection. The main workflow of LSR-based object detection is introduced. To analyze the performance of LSR, we perform explicit experiments and systematically discuss the interplay of additional noise with the system parameters. LSR is proven to be helpful in detecting weak objects from low-quality underwater images. Both OU noise and extra delay loop will help the whole system to maintain stability in a higher noisy background.

Fractional Ornstein–Uhlenbeck noise

Fractional Ornstein–Uhlenbeck noise is considered and investigated. The fractional Ornstein–Uhlenbeck noise may be linked with a supercapacitor driven by the white noise, and its correlation function for the stationary state shows monotonic and oscillatory decays. In the case of the oscillatory behavior the correlation function presents behaviors similar to those of the harmonic noise (harmonic oscillator driven by the white noise). For application, the Langevin equation with the harmonic potential driven by the fractional Ornstein–Uhlenbeck noise is considered; the first two moments and mean energy are investigated.

Analyzing a stochastic process driven by Ornstein-Uhlenbeck noise.

A scalar Langevin-type process X(t) that is driven by Ornstein-Uhlenbeck noise η(t) is non-Markovian. However, the joint dynamics of X and η is described by a Markov process in two dimensions. But even though there exists a variety of techniques for the analysis of Markov processes, it is still a challenge to estimate the process parameters solely based on a given time series of X. Such a partially observed 2D process could, e.g., be analyzed in a Bayesian framework using Markov chain Monte Carlo methods. Alternatively, an embedding strategy can be applied, where first the joint dynamics of X and its temporal derivative X[over ̇] is analyzed. Subsequently, the results can be used to determine the process parameters of X and η. In this paper, we propose a more direct approach that is purely based on the moments of the increments of X, which can be estimated for different time-increments τ from a given time series. From a stochastic Taylor expansion of X, analytic expressions for these moments can be derived, which can be used to estimate the process parameters by a regression strategy.

Diffusion of Brownian particles in a tilted periodic potential under the influence of an external Ornstein–Uhlenbeck noise

The diffusion behaviors of Brownian particles in a tilted periodic potential under the influence of an internal white noise and an external Ornstein–Uhlenbeck noise are investigated through numerical simulation. In contrast to the case when the bias force is smaller or absent, the diffusion coefficient exhibits a nonmonotonic dependence on the correlation time of the external noise when bias force is large. A mechanism different from locked-to-running transition theory is presented for the diffusion enhancement by a bias force in intermediate to large damping. In the underdamped regime and the presence of external noise, the diffusion coefficient is a monotonically decreasing function of low temperature rather than a nonmonotonic function when external noise is absent. The diffusive process undergoes four regimes when bias force approaches but is less than its critical value and noises intensities are small. These behaviors can be attributed to the locked-to-running transition of particles.

Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics.

Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional density evolution, there exists another type of discrete evolution that may not correspond to a continuous, real dynamical counterpart. This virtual dynamics case is also able to produce the desired stationary distribution. Different types of repartition lead to different numerical schemes, of which the accuracy and efficiency are investigated through studying the harmonic oscillator potential, an analytical solvable model. By analyzing the asymptotic distribution and characteristic correlation time that are derived by either directly solving the discrete equations of motion or using the related phase space propagators, it is shown that the optimal friction coefficient resulting in the minimum characteristic correlation time depends on the time interval chosen in the numerical implementation. When the recommended "middle" scheme is employed, both analytical and numerical results demonstrate that, for good numerical performance in efficiency as well as accuracy, one may choose a friction coefficient in a wide range from around the optimal value to the high friction limit.

Enhancement of Quantum Correlations in Qubit-Qutrit Systems under the non-Markovian Environment**Supported by the National Natural Science Foundation of China under Grant Nos. 11274132 and 11550110180

We investigate the time evolution of quantum correlations of a hybrid qubit-qutrit system under the classical Ornstein-Uhlenbeck (OU) noise. Here we consider two different one-parameter families of qubit-qutrit states which independently interact with the non-Markovian reservoirs. A comparison with the Markovian dynamics reveals that for the same set of initial condition parameters, the non-Markovian behavior of the environment plays an important role in the enhancement of the survival time of quantum correlations. In addition, it is observed that the non-Markovian strength has a positive impact on the correlations time. For the initial separable states it is found that there is a finite time interval in which the geometric quantum discord is frozen despite the presence of a noisy environment and that interval can be further prolonged by using the non-Markovian property. Moreover, its decay can be significantly delayed.

Decoherence and tripartite entanglement dynamics in the presence of Gaussian and non-Gaussian classical noise

We address the entanglement dynamics of a three-qubit system interacting with a classical fluctuating environment described either by a Gaussian or non-Gaussian noise in three different configurations namely: common, independent and mixed environments. Specifically, we focus on the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise (RTN). The qubits are prepared in a state composed of a Greenberger-Horne-Zeilinger (GHZ) and a W state. With the help of the tripartite negativity, we show that the entanglement evolution is not only affected by the type of system-environment coupling but also by the kind and the memory properties of the considered noise. We also compared the dynamics induced by the two kinds of noise and we find that even if both noises have a Lorentzian spectrum, the effects of the OU noise cannot be in a simple way deduced from those of the RTN and vice-versa. In addition, we show that the entanglement can be indefinitely preserved when the qubits are coupled to the environmental noise in a common environment (CE). Finally, the presence or absence of peculiar phenomena such as entanglement revivals (ER) and entanglement sudden death (ESD) is observed.

The Dynamics of Quantum Correlations in Mixed Classical Environments

We present a comparative study of the dynamics of entanglement and quantum discord in a bipartite system in the presence of mixed classical noises. In particular, the joint effects of three different types of classical noises, namely, random telegraphic noise (RTN), Ornstein–Uhlenbeck noise (OU), and static noise, are studied by combining them in two different ways. In each case, one marginal system is coupled with random telegraphic noise, and the other marginal system is coupled with either OU or static noise. We make a comparison between the behaviors of both correlations in the two setups. In the weak coupling regime, the qualitative behavior of entanglement is unaffected by switching the coupling of only one marginal system from OU to static noise, and vice versa. However, the behavior of quantum discord strongly depends on whether it is coupled with OU or static noise. On the other hand, in the strong coupling regime, the static noise is more fatal to the survival of both correlations as compared to the other two noises.

Stochastically forced dislocation density distribution in plastic deformation

The dynamical evolution of dislocations in plastically deformed metals is controlled by both deterministic factors arising out of applied loads and stochastic effects appearing due to fluctuations of internal stress. Such types of stochastic dislocation processes and the associated spatially inhomogeneous modes lead to randomness in the observed deformation structure. Previous studies have analyzed the role of randomness in such textural evolution, but none of these models have considered the impact of a finite decay time (all previous models assumed instantaneous relaxation which is "unphysical") of the stochastic perturbations in the overall dynamics of the system. The present article bridges this knowledge gap by introducing a colored noise in the form of an Ornstein-Uhlenbeck noise in the analysis of a class of linear and nonlinear Wiener and Ornstein-Uhlenbeck processes that these structural dislocation dynamics could be mapped on to. Based on an analysis of the relevant Fokker-Planck model, our results show that linear Wiener processes remain unaffected by the second time scale in the problem, but all nonlinear processes, both the Wiener type and Ornstein-Uhlenbeck type, scale as a function of the noise decay time τ. The results are expected to ramify existing experimental observations and inspire new numerical and laboratory tests to gain further insight into the competition between deterministic and random effects in modeling plastically deformed samples.

Escape rate of Brownian particles from a metastable potential well under time derivative Ornstein-Uhlenbeck noise

We investigate the escape rate of Brownian particles that move in a cubic metastable potential subjected to an internal time derivative Ornstein-Uhlenbeck noise (DOUN). This noise can induce the ballistic diffusion of force-free Brownian particles. Some new features are found. The escape rate for DOUN shows qualitative different dependence on potential well width compared with OUN which induces normal diffusion. As the potential barrier height decreases, the escape rate of DOUN deviates from Arrhenius law considerably earlier than that of Ornstein-Uhlenbeck noise (OUN). The Brownian particles escape faster under DOUN than that under OUN. A quasi-periodic oscillation occurs in transient state. A solvable case is presented to demonstrate the significant cancellation behavior in the barrier region that governs most of these phenomena. The physical mechanism of the findings can be clarified by the noise features. These characteristics should be common for internal noises that induce superdiffusion, especially the ballistic diffusion.

The simulation of the non-Markovian behaviour of a two-level system

Non-Markovian relaxation dynamics of a two-level system is studied with the help of the non-linear stochastic Schrödinger equation with coloured Ornstein–Uhlenbeck noise. This stochastic Schrödinger equation is investigated numerically with an adapted Platen scheme. It is shown, that the memory effects have a significant impact to the dynamics of the system.

On enhancement of vibration-based energy harvesting by a random parametric excitation

An electromechanical linear oscillator with a random ambient excitation and telegraphic noise parametric excitation is considered as an energy harvester model. It is shown that a parametric colored excitation can have a dramatic effect on the enhancement of the energy harvesting. A close relation with mean-square stability of the oscillator is established. Four sources of the ambient excitation are considered: the white noise, the Ornstein–Uhlenbeck noise, the harmonic noise and the periodic function. Analytical expressions for stationary electrical net mean power are presented for all the considered cases, confirming the proposed approach.

Open quantum system stochastic dynamics with and without the RWA

We study the dynamics of a two-level quantum system interacting with a single frequency electromagnetic field and a stochastic magnetic field, with and without making the rotating wave approximation (RWA). The transformation to the rotating frame does not commute with the stochastic Hamiltonian if the stochastic field has nonvanishing components in the transverse direction, hence, applying the RWA requires transformation of the stochastic terms in the Hamiltonian. For Gaussian white noise, the master equation is derived from the stochastic Schrödinger–Langevin equations, with and without the RWA. With the RWA, the master equation for the density matrix has Lindblad terms with coefficients that are time-dependent (i.e., the master equation is time-local). An approximate analytic expression for the density matrix is obtained with the RWA. For Ornstein–Uhlenbeck noise, as well as other types of colored noise, in contradistinction to the Gaussian white noise case, the non-commutation of the RWA transformation and the noise Hamiltonian can significantly affect the RWA dynamics when , where ω is the electromagnetic field frequency and is the stochastic magnetic field correlation time.

Evolution of Genuine Multipartite Entanglement of Specific and Random States Under non-Markovian Noise

We study the dynamics of genuine multipartite entanglement under non-Markovian noise. Using a computable entanglement monotone for multipartite systems, we investigate a system of three qubits each of which is individually exposed to classical Ornstein–Uhlenbeck noise. We found that the W state mixed with the maximally mixed state is the most fragile state, whereas a similar mixture of GHZ state exhibits robust behaviour. We compare dynamics of these states with dynamics of similar mixtures of random states and weighted graph states. We also discuss the limiting cases.

The Smoluchowski-Kramers Limit of Stochastic Differential Equations with Arbitrary State-Dependent Friction

We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our systems have arbitrary state-dependent friction and noise coefficients. We identify the limiting equation and, in particular, the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation. The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter. The result is sufficiently general to include systems driven by both white and Ornstein-Uhlenbeck colored noises. We discuss applications of the main theorem to several physical phenomena, including the experimental study of Brownian motion in a diffusion gradient.