Search results for "NOISE"

Random walk approach to the analytic solution of random systems with multiplicative noise—The Anderson localization problem

2006

We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from delocalized to localized states is treated as a generalized diffusion with a noise-induced first-order phase transition. The generalized diffusion manifests itself in the divergence of averages of wavefunctions (correlators). This divergence is controlled by the Lyapunov exponent $\gamma$, which is the inverse of the localization length, $\xi=1/\gamma$. The appearance of the generalized diffusion arises due to the instability of a fundamental mode corresponding to…

Zeno dynamics and high-temperature master equations beyond secular approximation

2013

Complete positivity of a class of maps generated by master equations derived beyond the secular approximation is discussed. The connection between such class of evolutions and physical properties of the system is analyzed in depth. It is also shown that under suitable hypotheses a Zeno dynamics can be induced because of the high temperature of the bath.

Escape from a metastable state with fluctuating barrier

2003

Abstract We investigate the escape of a Brownian particle from fluctuating metastable states. We find the conditions for the noise enhanced stability (NES) effect for periodical driving force. We obtain general equations useful to calculate the average escape time for randomly switching potential profiles. For piece-wise linear potential profile we reveal the noise enhanced stability (NES) effect, when the height of “reverse” potential barrier of metastable state is comparatively small. We obtain analytically the condition for the NES phenomenon and the average escape time as a function of parameters, which characterize the potential and the driving dichotomous noise.

Tuning active Brownian motion with shot noise energy pulses

2009

The main aim of this work is to explore the possibility of modeling the biological energy support mediated by absorption of ATP (adenosine triphosphate) as an energetic shot noise. We develop a general model with discrete input of energy pulses and study shot-noise-driven ratchets. We consider these ratchets as prototypes of Brownian motors driven by energy-rich ATP molecules. Our model is a stochastic machine able to acquire energy from the environment and convert it into kinetic energy of motion. We present characteristic features and demonstrate the possibility of tuning these motors by adapting the mean frequency of the discrete energy inputs, which are described as a special shot noise…

Memory effect and generation-recombination noise of magnetic monopoles in spin ice

2019

Noise driven translocation of short polymers in crowded solutions

2008

In this work we study the noise induced effects on the dynamics of short polymers crossing a potential barrier, in the presence of a metastable state. An improved version of the Rouse model for a flexible polymer has been adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and introducing a Lennard-Jones potential between all beads. A bending recoil torque has also been included in our model. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion with a Gaussian uncorrelated noise. We find a nonmonotonic behaviour of the mean first passage time and the most probable tran…

The problem of analytical calculation of barrier crossing characteristics for Levy flights

2008

By using the backward fractional Fokker-Planck equation we investigate the barrier crossing event in the presence of Levy noise. After shortly review recent results obtained with different approaches on the time characteristics of the barrier crossing, we derive a general differential equation useful to calculate the nonlinear relaxation time. We obtain analytically the nonlinear relaxation time for free Levy flights and a closed expression in quadrature of the same characteristics for cubic potential.

Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

2012

Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.

A simple comparative analysis of exact and approximate quantum error correction

2014

We present a comparative analysis of exact and approximate quantum error correction by means of simple unabridged analytical computations. For the sake of clarity, using primitive quantum codes, we study the exact and approximate error correction of the two simplest unital (Pauli errors) and nonunital (non-Pauli errors) noise models, respectively. The similarities and differences between the two scenarios are stressed. In addition, the performances of quantum codes quantified by means of the entanglement fidelity for different recovery schemes are taken into consideration in the approximate case. Finally, the role of self-complementarity in approximate quantum error correction is briefly ad…

Rough nonlocal diffusions

2019

We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with "common" noise. To study the equation we build a self-contained framework of non-linear rough integration theory which we use to study McKean-Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the corresponding Fokker-Planck equation and prove well-posedness.