Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Lecture notes in mathematics

Stratonovich solution of a quantum stochastic differential equation describing light emission and absorption

Wilhelm von Waldenfels

Published Jan 1, 1985• 6 citations
Publisher
DOI
10.1007/bfb0101543

Related papers

Ito solution of the linear quantum stochastic differential equation describing light emission and absorption

Wilhelm von Waldenfels

Lecture notes in mathematics•Jan 1, 1984•25 citations

Spontaneous light emission described by a quantum stochastic differential equation

Wilhelm von Waldenfels

Lecture notes in mathematics•Jan 1, 1985•2 citations

Quantum Stratonovich calculus and the quantum Wong-Zakai theorem

John Edward Gough

We extend the Itō-to-Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Itō one and give conditions for the existence of Stratonovich time-ordered exponentials. We show that conversion formula for the coefficients has a striking resemblance to Green’s function formulas from standard perturbation theory. We show that the calculus conveniently describes the Markov limit of regular open quantum dynamical systems in much the same way as in the Wong-Zakai approximation theorems of classical stochastic analysis. We extend previous limit results to multiple-dimensions with a proof that makes use of diagrammatic conventions.

arXiv:math-ph/0511046•Journal of Mathematical Physics•Nov 1, 2006•33 citations

Applying the CSL Stratonovich Equation to the Free Particle Undergoing Collapse in Position

Philip Pearle

Abstract This chapter addresses the problem of applying the continuous spontaneous localization (CSL) Stratonovich equation to the free particle undergoing collapse in position, by finding the solution in Gaussian form. This solution was previously obtained in Chapter 10 by using the linear Schrödinger equation/probability rule formulation of CSL (which was used in the first seven chapters of this book). This chapter shows how the same result is obtained from the stochastic differential equation formulation of CSL.

•Jan 30, 2024•0 citations

The Stratonovich Interpretation of Quantum Stochastic Approximations

John Edward Gough

Potential Analysis•Nov 1, 1999•10 citations

Solution of the quantum liouville equation as a stochastic process

Sarah John, Edward A. Remler

Annals of Physics•Nov 1, 1987•32 citations
We extend the Itō-to-Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Itō one and give conditions for the existence of Stratonovich time-ordered exponentials. We show that conversion formula for the coefficients has a striking resemblance to Green’s function formulas from standard perturbation theory. We show that the calculus conveniently describes the Markov limit of regular open quantum dynamical systems in much the same way as in the Wong-Zakai approximation theorems of classical stochastic analysis. We extend previous limit results to multiple-dimensions with a proof that makes use of diagrammatic conventions.
Abstract This chapter addresses the problem of applying the continuous spontaneous localization (CSL) Stratonovich equation to the free particle undergoing collapse in position, by finding the solution in Gaussian form. This solution was previously obtained in Chapter 10 by using the linear Schrödinger equation/probability rule formulation of CSL (which was used in the first seven chapters of this book). This chapter shows how the same result is obtained from the stochastic differential equation formulation of CSL.