相关论文: A Variance Reduction Technique for the Stochastic …

An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to…

Based on recently derived exact stochastic Liouville-von Neumann equations, several strategies for the efficient simulation of open quantum systems are developed and tested on the spin-boson model. The accuracy and efficiency of these…

The non-Markovian dynamics of open quantum systems is still a challenging task, particularly in the non-perturbative regime at low temperatures. While the Stochastic Liouville-von Neumann equation (SLN) provides a formally exact tool to…

We develop a real-time Full Configuration Interaction Quantum Monte Carlo approach for the modeling of driven-dissipative open quantum systems. The method enables stochastic sampling of the Liouville-von-Neumann time evolution of the…

Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…

We consider a natural dimension reduction technique for the Liouville-von Neumann equation for a mixed quantum system based on evaluation of a trace formula combined with a direct expansion in modified Chebyshev polynomials. This reduction…

Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic…

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us…

We apply the stochastic variational method to the action of the ideal fluid and showed that the Navier-Stokes equation is derived. In this variational method, the effect of dissipation is realized as the direct consequence of the…

A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…

Previously developed ``stochastic representation of deterministic interactions`` enables exact treatment of an open system without leaving its native phase space (Hilbert space) due to peculiar stochastic extension of the Liouville (von…

Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…

The statistical counterpart of the formalism of hamiltonian systems with convex dissipation arXiv:0810.1419 , arXiv:1408.3102 is a completely open subject. Here are described a stochastic version of the SBEN principle and a Liouville type…

This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational principles yield deterministic as well as stochastic constrained…

In open quantum systems, the Liouvillian gap characterizes the relaxation time toward the steady state. However, accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the…

In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…

Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These…

Stochastic Variational Method (SVM) is the generalization of the variation method to the case with stochastic variables. In the series of papers, we investigate the applicability of SVM as an alternative field quantization scheme. Here, we…

Langevin (stochastic differential) equations are routinely used to describe particle-laden flows. They predict Gaussian probability density functions (PDFs) of a particle's trajectory and velocity, even though experimentally observed…

In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…