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The two-site Holstein model represents a first non-trivial paradigm for the interaction between an itinerant charge with a quantum oscillator, a very common topic in different ambits. Exact results can be achieved both analytically and…

Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed…

We develop an information-theoretic formulation of stochastic dynamics in which the fundamental stochastic variable is the total action connecting spacetime points, rather than individual paths. By maximizing Shannon entropy over a joint…

Stochastic mechanics is based on the hypothesis that all matter is subject to universal modified Brownian motion. In this report, we calculated probability density distributions using concepts of stochastic mechanics independent of…

Ehrenfest, Born-Oppenheimer, Langevin and Smoluchowski dynamics are shown to be accurate approximations of time-independent Schr\"odinger observables for a molecular system avoiding caustics, in the limit of large ratio of nuclei and…

We present a detailed account of the technical aspects of stochastic quantum molecular dynamics, an approach introduced recently by the authors [H. Appel and M. Di Ventra, Phys. Rev. B 80 212303 (2009)] to describe coupled electron-ion…

We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics…

Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac-Zwanzig setting, with the initial data for the electrons stochastically perturbed…

Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…

We propose a model for a molecular junction with internal anharmonic torsional vibrations interacting with an electric current. The Wangsness-Bloch-Redfield master equation approach is used to determine the stationary reduced density matrix…

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie…

Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional…

Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…

We investigate the properties of the molecular quantum dot (Holstein-Anderson) model using numerical and analytical techniques. Path integral Monte Carlo simulations for the cumulants of the distribution function of the phonon coordinate…

We extend the Landauer-B\"uttiker probe formalism for conductances to the high bias regime, and study the effects of environmentally-induced elastic and inelastic scattering on charge current in single molecule junctions, focusing on…

Understanding phononic heat transport processes in molecular junctions is a central issue in the developing field of nanoscale heat conduction and manipulation. Here we present a Stochastic Nonequlibrium Molecular Dynamics simulation…

In the past decades, Random Electrodynamics (also called Stochastic Electrodynamics) has been used to study the classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation. Random Electrodynamics (RED)…

We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…

Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…

Stochastic Gradient Descent (SGD) is commonly modeled as a Langevin process, assuming that minibatch noise acts as Brownian motion. However, this approximation relies on a continuous-time limit and a sqrt(eta) noise scaling that does not…