A generalized Langevin equation with fluctuating diffusivity (GLEFD) is proposed, and it shown that the GLEFD satisfies a fluctuation-dissipation relation. If memory kernel power law, exhibits subdiffusion, non-Gaussianity, stretched-exponential relaxation. The case in which given by single exponential function also investigated as an analytically tractable example. In particular, mean-square d...

We consider the trajectories of particles diffusing between two infinite baths of fixed concentrations connected by a channel, e.g., a protein channel of a biological membrane. The steady state influx and efflux of Langevin trajectories at the boundaries of a finite volume containing the channel and parts of the two baths is replicated by termination of outgoing trajectories and injection accor...

The problem of controlling quantum stochastic evolutions arises naturally in several different fields such as quantum chemistry, quantum information theory, quantum engineering, etc. In this paper, we apply the recently discovered closed form of the unitarity conditions for stochastic evolutions driven by the square of white noise [9] to solve this problem in the case of quadratic cost function...

A prescription is given for performing numerical simulations of field theory in Minkowski space using the Langevin equation. By introducing a weak damping term we find that the Langevin equations relax to their equilibrium values in a rather modest amount of time. As an example, we calculate the Green functions for both the harmonic and anharmonic oscillators. We study both analytically and num...