Related papers: Collapse models with non-white noises II: particle…
We consider a stochastically forced nonlinear oscillator driven by a stationary Gaussian noise that has an algebraically decaying covariance function. It is well known that such noise processes can be renormalized to converge to fractional…
We investigate cosmological models described by a scalar field with an exponential potential, and apply the stochastic formalism, which allows us to study how quantum field fluctuations give rise to stochastic noise. This modifies the…
Inspired by the notion that environmental noise is in principle observable, whilst fundamental noise due to spontaneous localisation would not be, we study the estimation of the diffusion parameter induced by wave function collapse models…
We study effects of independent white noise on synchronization phenomena in ensembles of coupled limit cycle oscillators with different native frequencies. We consider a simple model where the ensemble consists of two inter-connected…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
A typical feature of spontaneous collapse models which aim at localizing wavefunctions in space is the violation of the principle of energy conservation. In the models proposed in the literature the stochastic field which is responsible for…
Selected issues of the concept of spontaneous collapse are discussed, with the emphasis on the gravity-related model. We point out that without spontaneous collapses the Schr\"odinger cat states would macroscopically violate the standard…
We develop a quantum field theory based on random nonHermitian actions, which upon quantization lead to stochastic nonlinear Schr\"{o}dinger dynamics for the state vector. In this framework, Lorentz and spacetime translation symmetries are…
Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
We study a stochastically driven, damped nonlinear oscillator whose frequency is modulated by a white or coloured noise. Using diagrammatic perturbation theory, we find that in the absence of nonlinearity, parametric modulation by a…
We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a Time-Dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled…
We present a new stochastic differential equation model for the spontaneous emission noise and carrier noise in semiconductor lasers. The correlations between these two types of noise have often been neglected in recent studies of the…
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…
The Van der Pol equation is a paradigmatic model of relaxation oscillations. This remarkable nonlinear phenomenon of self-sustained oscillatory motion underlies important rhythmic processes in nature and electrical engineering. Relaxation…
In a noisy environment, oscillations loose their coherence which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional…
Wavefunction collapse models modify Schr\"odinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum…
We study a spontaneous collapse model for a two-level (spin) system, in which the Hamiltonian and the stochastic terms do not commute. The numerical solution of the equations of motions allows to give precise estimates on the regime at…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
In this paper, we consider a system of $k$ second order non-linear stochastic partial differential equations with spatial dimension $d \geq 1$, driven by a $q$-dimensional Gaussian noise, which is white in time and with some spatially…