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Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
Modeling car-following behavior is fundamental to microscopic traffic simulation, yet traditional deterministic models often fail to capture the full extent of variability and unpredictability in human driving. While many modern approaches…
A number of non-Markovian stochastic Schr\"odinger equations, ranging from the numerically exact hierarchical form towards a series of perturbative expressions sequentially presented in an ascending degrees of approximations are revisited…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
Quantum walks in dynamically-disordered networks have become an invaluable tool for understanding the physics of open quantum systems. In this work, we introduce a novel approach to describe the dynamics of indistinguishable particles in…
A quantum stochastic model for an open dynamical system (quantum receiver) and output multi-channel of observation with an additive nonvacuum quantum noise is given. A quantum stochastic Master equation for the corresponding instrument is…
This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
Spectral line-shapes provide a window into the local environment coupled to a quantum transition in the condensed phase. In this paper, we build upon a stochastic model to account for non-stationary background processes produced by…
Disorder, noise and interaction play a crucial role in the transport properties of real systems, but they are typically hard to control and study both theoretically and experimentally, especially in the quantum case. Here we explore a…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
Simulating charge and energy transfer in extended molecular networks requires an effective model to include the environment because it significantly affects the quantum dynamics. A prototypical effect known as Environment-Assisted Quantum…
We study the problem of calculating transport properties of interacting quantum systems, specifically electrical and thermal conductivities, by computing the non-equilibrium steady state (NESS) of the system biased by contacts. Our approach…
We investigate out-of-equilibrium entanglement dynamics in a generalization of the so-called $QSSEP$ model, which is a free-fermion chain with stochastic in space and time hopping amplitudes. In our setup, the noisy amplitudes are…
Stunningly large exciton transfer rates in the light harvesting complex of photosynthesis, together with recent experimental 2D spectroscopic data, have spurred a vivid debate on the possible quantum origin of such efficiency. Here we show…
We present an overview of time-dependent transport phenomena in quantum systems, with a particular emphasis on steady-state regimes. We present the ideas after the main theoretical frameworks to study open-quantum systems out of…
This paper introduces a stochastic hybrid system (SHS) framework in state space model to capture sensor, communication, and system contingencies in modern power systems (MPS). Within this new framework, the paper concentrates on the…
We consider the description of quantum noise within the framework of the standard Copenhagen interpretation of quantum mechanics applied to a composite system environment setting. Averaging over the environmental degrees of freedom leads to…
A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic…
We present a Machine Learning approach to solve electronic quantum transport equations of one-dimensional nanostructures. The transmission coefficients of disordered systems were computed to provide training and test datasets to the…
Stochastic storage models based on essentially non-Gaussian noise are considered. The stochastic description of physical systems based on stochastic storage models is associated with generalized Poisson (or shot) noise, in which the jump…