Related papers: Stochastic Integral Representation for the Dynamic…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
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…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…
Symmetries are a key tool in understanding quantum systems, and, among many other things, can be exploited to increase the efficiency of numerical simulations of quantum dynamics. Disordered systems usually feature reduced symmetries and…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
We discuss a model of a system of interacting populations for the case when: (i) the growth rates and the coefficients of interaction among the populations depend on the populations densities: and (ii) the environment influences the growth…
The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic…
Quantum chaotic states over a noncommutative monoid, a unitalization of a noncommutative Ito algebra parametrizing a quantum stochastic Levy process, are described in terms of their infinitely divisible generating functionals over the…
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
This paper investigates the asymptotic behavior of stochastic recursive inclusions in the presence of non-zero, non-diminishing bias, a setting that frequently arises in zeroth-order optimization, stochastic approximation with…
Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to…
We investigate how free probability allows us to approximate the density of states in tight binding models of disordered electronic systems. Extending our previous studies of the Anderson model in neighbor interactions [J. Chen et al.,…
Simulating the dynamics of quantum many-body systems with disorder is a fundamental challenge. In this work, we propose a general approach -- the statistics-encoded tensor network (SeTN) -- to study such systems. By encoding disorder into…
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…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…