相关论文: The transport equation and zero quadratic variatio…

We study the transport of heat along a chain of particles interacting through a harmonic potential and subject to heat reservoirs at its ends. Each particle has two degrees of freedom and is subject to a stochastic noise that produces…

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…

We present a new method to introduce phase-space fluctuations in transport theories, corresponding to a full implementation of the Boltzmann-Langevin equation for fermionic systems. It is based on the procedure originally developed by Bauer…

We study a system of two coupled transport equations with freezing. The solutions freeze in time when they are equal. We prove existence and uniqueness of continuous solutions if the initial conditions are continuous. We discuss several…

It is shown that, in the absence of nodes and under regularity assumptions, a solution in a finite interval of time of the free Schroedinger equation solves a minimization problem which is a stochastic generalization of the classical…

We prove some theorems on the existence, uniqueness, stability and compactness properties of solutions to inhomogeneous transport equations with Sobolev coefficients, where the inhomogeneous term depends upon the solution through an…

A Langevin equation is proposed to describe the transport of overdamped Brownian particles in a periodic rough potential and driven by an unbiased periodic force. The equation can be transformed into the Fokker-Planck equation by using the…

In this paper, we established a quadratic transportation cost inequality for scalar stochastic conservation laws driven by multiplicative noise. The doubling variables method plays an important role.

We study the Navier-Stokes equations with transport noise in critical function spaces. Assuming the initial data belongs to $H^{1/2}$ almost surely, we establish the existence and uniqueness of a local-in-time probabilistically strong…

We consider the two dimensional Navier-Stokes equations in vorticity form with a stochastic forcing term given by a gaussian noise, white in time and coloured in space. First, we prove existence and uniqueness of a weak (in the Walsh sense)…

We present a stochastic approach for ion transport at the mesoscopic level. The description takes into account the self-consistent electric field generated by the fixed and mobile charges as well as the discrete nature of these latter. As…

The study of noise assisted transport in quantum systems is essential in a wide range of applications from near-term NISQ devices to models for quantum biology. Here, we study a generalised XXZ model in the presence of stochastic collision…

We consider the stochastic continuity equation driven by Brownian motion. We use the techniques of the Malliavin calculus to show that the law of the solution has a density with respect to the Lebesgue measure. We also prove that the…

The stochastic partial differential equation analyzed in this work is the Cahn-Hilliard equation perturbed by an additive fractional white noise (fractional in time and white in space). We work in the case of one spatial dimension and apply…

The Langevin equation with multiplicative noise and state-dependent transport coefficient has to be always complemented with the proper interpretation rule of the noise, such as the Ito and Stratonovich conventions. Although the…

We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…

We present a perspective of simple models of nonequilibrium directed transport described in terms of a Langevin equation formalism. We consider a Brownian particle under various circumstances and driven by thermal (equilibrium) and…

Nonergodic Brownian motion is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding either a vanishing or a divergent zero-frequency friction strength, the non-Markovian Browninan dynamics exhibits…

We introduce an elementary method for proving the absolute continuity of the time marginals of one-dimensional processes. It is based on a comparison between the Fourier transform of such time marginals with those of the one-step Euler…

Transport phenomena play a key role in a variety of application domains, and efficient simulation of these dynamics remains an outstanding challenge. While quantum computers offer potential for significant speedups, existing algorithms…