Related papers: Hermitian stochastic methodology for X-ray superfl…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called…
In this work we introduce a phase-space description based on the positive P representation for bosonic fields interacting with a system of quantum emitters. The formalism is applicable to collective light-matter interactions and open…
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…
The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given…
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and…
In this paper we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of…
Standard methods used for computing the dynamics of a quantum many-body system are the mean-field (MF) approximations such as the time-dependent Hartree-Fock (TDHF) approach. Even though MF approaches are quite successful, they suffer some…
This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free…
In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting pont is propagated separately using the Time-Dependent Hartree-Fock equation of…
Exceptional points, a remarkable phenomenon in physical systems, have been exploited for sensing applications. It has been demonstrated recently that it can also utilize as sensory threshold in which the interplay between exceptional-point…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain non-deterministic in…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
Modern observatories are designed to deliver increasingly detailed views of astrophysical signals. To fully realize the potential of these observations, principled data-analysis methods are required to effectively separate and reconstruct…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…