Memory-dependent noise-induced resonance and diffusion in non-markovian systems

Abstract

We study the random processes with non-local memory and obtain new solutions of the Mori-Zwanzig equation describing non-markovian systems. We analyze the system dynamics depending on the amplitudes $\nu$ and ${\mu }_0$ of the local and non-local memory and pay attention to the line in the ($\nu$, ${\mu }_0$)-plane separating the regions with asymptotically stationary and non-stationary behavior. We obtain general equations for such boundaries and consider them for three examples of the non-local memory functions. We show that there exist two types of the boundaries with fundamentally different system dynamics. On the boundaries of the first type, the diffusion with memory takes place, whereas on borderlines of the second type, the phenomenon of noise-induced resonance can be observed. A distinctive feature of noise-induced resonance in the systems under consideration is that it occurs in the absence of an external regular periodic force. It takes place due to the presence of frequencies in the noise spectrum, which are close to the self-frequency of the system. We analyze also the variance of the process and compare its behavior for regions of asymptotic stationarity and non-stationarity, as well as for diffusive and noise-induced-resonance borderlines between them.

arXiv comment11 pages, 6 figures

References in corpus (15)

• Non-Markovian effects on the dynamics of entanglement
• Quantum Metrology in Non-Markovian Environments
• Memory in network flows and its effects on spreading dynamics and community detection
• Quantum Semi-Markov Processes
• Origin of hyperdiffusion in generalized Brownian motion
• Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem
• Irreversible effects of memory
• A simple measure of memory for dynamical processes described by the generalized Langevin equation
• Exact closed master equation for Gaussian non-Markovian dynamics
• Equivalence between non-Markovian and Markovian dynamics in epidemic spreading processes
• Irreversible dynamics of a massive intruder in dense granular fluids
• Anomalous scaling of dynamical large deviations
• Mori-Zwanzig projection operator formalism for systems with time-dependent Hamiltonians
• Space-time velocity correlation function for random walks
• Continuous stochastic processes with non-local memory