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We develop a method to study quantum impurity models, small interacting quantum systems linearly coupled to an environment, in presence of an additional Markovian quantum bath, with a generic non-linear coupling to the impurity. We aim at…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…
We unravel the periodically driven dynamics of two repulsively interacting bosonic impurities within a bosonic bath upon considering either the impact of a finite pulse or a continuous shaking of the impurities harmonic trap. Following a…
Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
Stochastic representation for interaction of quantum systems is formulated which allows to replace some of them by equivalent but purely commutative random sources. The formalism is applied to two-level systems interacting with Gaussian…
The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…
Kinematic sensors are often used to analyze movement behaviors in sports and daily activities due to their ease of use and lack of spatial restrictions, unlike video-based motion capturing systems. Still, the generation, and especially the…
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…
The spin-boson model, describing a two-level system strongly coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong…
Using a generalized energy-conserving transition probability, it is shown how nonadiabatic calculations, within the Wigner-Heisenberg representation of quantum mechanics, can be reliably extended to far longer times than those allowed by a…
Using Stokesian dynamics simulations, we examine the flow of a monodisperse, neutrally buoyant, homogeneous suspension of non-Brownian solid spheres in simple shear, starting from a large number of independent hard-sphere distributions and…
Closure modeling - the statistical modeling of missing dynamics in the natural sciences and engineering - is a growing and active area of research. Existing methods for closure modeling are often computationally prohibitive, lack…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…
Without access to the full quantum state, modeling dissipation in an open system requires approximations. The physical soundness of such approximations relies on using realistic microscopic models of dissipation that satisfy completely…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
We extend a standard stochastic theory to study open quantum systems coupled to generic quantum environments including the three fundamental classes of noninteracting particles: bosons, fermions and spins. In this unified stochastic…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…