Related papers: Memory-dependent noise-induced resonance and diffu…
In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable…
This paper concerns about the large time behavior of acoustic wave motion driven by a random force acting through the boundary. We begin with an abstract result showing the interconnection between the regularity of Markov semigroup…
We investigate a nonlinear dynamical system which ``remembers'' preselected values of a system parameter. The deterministic version of the system can encode many parameter values during a transient period, but in the limit of long times,…
We study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their commonly studied statistics such as the mean square distance. This…
Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…
It has been proposed that neural noise in the cortex arises from chaotic dynamics in the balanced state: in this model of cortical dynamics, the excitatory and inhibitory inputs to each neuron approximately cancel, and activity is driven by…
Recently Segev et al. (Phys. Rev. E 64,2001, Phys.Rev.Let. 88, 2002) made long-term observations of spontaneous activity of in-vitro cortical networks, which differ from predictions of current models in many features. In this paper we…
Light scattering from resonantly or nearly resonantly excited systems, known as resonance fluorescence, has been gaining importance as a versatile tool for investigating quantum states of matter and readout of quantum information, recently…
This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is…
We show that the NLS systems with multiplicative noise, nonlinear damping and nonlocal dispersion exhibit a variety of interesting effects which may be useful for modelling the dynamical behavior of one- and two-dimensional molecular…
The understanding of memory effects arising from the interaction between system and environment is a key for engineering quantum thermodynamic devices beyond the standard Markovian limit. We study the performance of measurement-based…
We report on experiments addressing the non-linear interaction between a nano-mechanical mode and position fluctuations. The Duffing non-linearity transduces the Brownian motion of the mode, and of other non-linearly coupled ones, into…
A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal…
When high-frequency sound waves travel through media with anomalous diffusion, such as biological tissues, their motion can be described by nonlinear wave equations of fractional higher order. These can be understood as nonlocal…
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…
We report the first observation of non-Markovian stochastic resonance, i.e., noise-assisted amplification of a periodic signal in a system with memory. Our system is an oil-filled optical microcavity which, driven by a continuous wave…
Quantum non-Markovianity modifies the environmental decoherence of a system. This situation is enriched in complex systems owing to interactions among subsystems. We consider the problem of distinguishing the multiple sources of…
We consider the dynamics of strongly localized systems subject to dephasing noise with arbitrary correlation time. Although noise inevitably induces delocalization, transport in the noise-induced delocalized phase is subdiffusive in a…
We explore the possibility to generate nonlocal dynamical maps of an open quantum system through local system-environment interactions. Employing a generic decoherence process induced by a local interaction Hamiltonian, we show that initial…
The electron-phonon interaction is one of the most fundamental mechanisms in condensed matter physics. Phonons can induce memory effects in solid-state platforms when localized electronic states interact with lattice vibrations in…