We consider the nonlinear Schrödinger–Langevin equation for both signs of logarithmic nonlinearity. explicitly compute dynamics Gaussian solutions large times, which is obtained through study a particular differential order 2. then give asymptotic behavior general energy weak under some regularity assumptions. Some numerical simulations are performed in to corroborate theoretical results.

We propose a criterion for the validity of semiclassical gravity ~SCG! which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equatio...

We construct a theory for the (1+1)-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the first part of this work the classical Langevin equations of motion, governing the nonrelativistic dynamics of a free Brownian particle in the presence of a he...

In order to investigate dynamical symmetry breaking, we study Nambu·JonaLasinio model in the large-N limit in the stochastic quantization method. Here in order to solve Langevin equation, we impose specified initial conditions and construct “effective Langevin equation” in the large-N limit and give the same non-perturbative results as path-integral approach gives. Moreover we discuss stability...

We present a technique to resolve the rare event problem for a Langevin equation describing a system with thermally activated transitions. A transition event within a given time interval (0,t(f)) can be described by a transition path that has an activation part during (0,t(M)) and a deactivation part during (t(M),t(f))(0<t(M)<t(f)). The activation path is governed by a Langevin equation with ne...