Related papers: Collapse models with non-white noises
We show that uncorrelated Gaussian noise, despite its paradigmatic association with thermal equilibrium, can drive a system out of equilibrium and can serve as a resource from which work can be extracted. We consider an overdamped particle…
A stochastic second-order wave model is applied to assess the statistical properties of wave orbital velocity in random sea states below the water surface. Directional spreading effects as well as the dependency of the water depth are…
Instability-induced random branching of deterministic dynamics is discussed as a possible mechanism of random wave function collapse. In the case of two level systems, the Born probability rule emerges as the simplest linear solution to the…
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…
The spontaneous localization mechanism of collapse models induces a Brownian motion in all physical systems. This effect is very weak, but experimental progress in creating ultracold atomic systems can be used to detect it. In this paper,…
We seek an extension to Schrodinger's equation that incorporates the macroscopic measurement-induced wavefunction collapse phenomenon. We find that a suitable hybrid between two leading approaches, the Bohm-de Broglie pilot-wave and…
This paper deals with linear stochastic partial differential equations with variable coefficients driven by L\'{e}vy white noise. We first derive an existence theorem for integral transforms of L\'{e}vy white noise and prove the existence…
We propose, as an alternative theory of quantum mechanics, a relativistically covariant variational principle (VP) capable of describing both wavefunction collapse and, as an appropriate limiting case, evolution of the wavefunction…
This is an overview about natural sample spaces for differential equations driven by various noises. Appropriate sample spaces are needed in order to facilitate a random dynamical systems approach for stochastic differential equations. The…
Waves and oscillations are commonly observed in the dynamics of self-driven agents such as pedestrians or vehicles. Interestingly, many factors may perturb the stability of space homogeneous streaming, leading to the spontaneous formation…
In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability…
Time-irreversibility is a distinctive feature of non-equilibrium dynamics and several measures of irreversibility have been introduced to assess the distance from thermal equilibrium of a stochastically driven system. While the dynamical…
We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper [K.…
A system with two correlated Gaussian white noises is analysed. This system can describe both stochastic localization and long tails in the stationary distribution. Correlations between the noises can lead to a nonmonotonic behaviour of the…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…
One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schroedinger evolution by implementing spontaneous collapses of the wave function. An explicit…
We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…
We carry out a detailed study of dynamic multiscaling in the turbulent nonequilibrium, but statistically steady, state of the stochastically forced one-dimensional Burgers equation. We introduce the concept of $\textit{interval collapse…
A stochastic model for nondemolition continuous measurement in a quantum system is given. It is shown that the posterior dynamics, including a continuous collapse of the wave function, is described by a nonlinear stochastic wave equation.…
Using complex quantum Hamilton-Jacobi formulation, a new kind of non-linear equations is proposed that have almost classical structure and extend the Schroedinger equation to describe the collapse of the wave function as a finite-time…