Randomized Hamiltonian Feynman integrals and Schroedinger-Ito stochastic equations

TL;DR

This paper develops a novel stochastic Feynman path integral framework to represent solutions of two-dimensional white noise stochastic Schrödinger equations, advancing the mathematical tools for open quantum system analysis.

Contribution

It introduces a generalized Feynman integral approach for stochastic Schrödinger equations with white noise, providing new representations for open quantum system dynamics.

Findings

Representation of solutions via stochastic Feynman integrals

Application to continuous measurement in quantum systems

Enhanced mathematical understanding of stochastic quantum evolutions

Abstract

In this paper, we consider stochastic Schroedinger equations with two-dimensional white noise. Such equations are used to describe the evolution of an open quantum system undergoing a process of continuous measurement. Representations are obtained for solutions of such equations using a generalization to the stochastic case of the classical construction of Feynman path integrals over trajectories in the phase space.