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In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings, or to…
Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
We study a chain of non-linear, interacting spins driven by a static and a time-dependent magnetic field. The aim is to identify the conditions for the locally and temporally controlled spin switching. Analytical and full numerical…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
The methodology of stochastic description for dissipation, a generic scheme to decouple the interaction between two subsystems, is applied to the study of dissipative dynamics in quantum optics. It is shown that the influence of the coupled…
The Stochastic Liouville-von Neumann equation provides an exact numerical simulation strategy for quantum systems interacting with Gaussian reservoirs [J.T. Stockburger & H. Grabert, PRL 88, 170407 (2002)]. Its scaling with the extension of…
A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing…
We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after…
We study a spontaneous collapse model for a two-level (spin) system, in which the Hamiltonian and the stochastic terms do not commute. The numerical solution of the equations of motions allows to give precise estimates on the regime at…
A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of…
Stochastic uncertainties in complex dynamical systems lead to variability of system states, which can in turn degrade the closed-loop performance. This paper presents a stochastic model predictive control approach for a class of nonlinear…
The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
Numerical relativity simulations are essential to study the last stages of the binary neutron star coalescence. Unfortunately, for stable simulations there is the need to add an artificial low-density atmosphere. Here we discuss a new…