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A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus [PDF]

Entropy
We present a simple argument to derive the transformation of the quantum stochastic calculus formalism between inertial observers and derive the quantum open system dynamics for a system moving in a vacuum (or, more generally, a coherent) quantum field ...
John E. Gough
doaj   +7 more sources

Quantum stochastic calculus with maximal operator domains [PDF]

Annals of Probability, 2004
The purpose of this paper is to introduce a new formulation in quantum stochastic (QS) calculus and to unify the following two existent approaches: one closely related to classical Itô calculus; and the other to noncausal stochastic analysis and Malliavin calculus.
Stéphane Attal, J Martin Lindsay
exaly   +5 more sources

Quantum stochastic calculus and quantum nonlinear filtering

Journal of Multivariate Analysis, 1992
A *-algebraic indefinite structure of quantum stochastic (QS) calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability conditions in an infinitely dimensional nuclear space. The class of nondemolition output QS processes in quantum open systems is characterized in terms of the QS ...
Belavkin, Viacheslav P
exaly   +5 more sources

An Introduction to Quantum Stochastic Calculus [PDF]

, 1992
An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification.
K R Parthasarathy
exaly   +3 more sources

A Stochastic Fractional Calculus with Applications to Variational Principles [PDF]

Fractal and Fractional, 2020
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes.
Houssine Zine, Delfim F. M. Torres
doaj   +2 more sources

Damped quantum interference using stochastic calculus [PDF]

Journal of Modern Optics, 2003
It is shown how the phase-damping master equation, either in Markovian and nonMarkovian regimes, can be obtained as an averaged random unitary evolution. This, apart from offering a common mathematical setup for both regimes, enables us to solve this equation in a straightforward manner just by solving the Schrodinger equation and taking the stochastic
Salgado, D., Sanchez-Gomez, J. L.
openaire   +3 more sources

PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black–Scholes Equation

Entropy, 2019
The Accardi–Boukas quantum Black–Scholes framework, provides a means by which one can apply the Hudson–Parthasarathy quantum stochastic calculus to problems in finance.
Will Hicks
doaj   +1 more source

Quantum stochastic calculus and the dynamical stark effect [PDF]

Reports on Mathematical Physics, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maassen, J.D.M., Robinson, P.A.
openaire   +4 more sources

On Quantum Statistical Mechanics: A Study Guide

Advances in Mathematical Physics, 2017
We provide an introduction to a study of applications of noncommutative calculus to quantum statistical physics. Centered on noncommutative calculus, we describe the physical concepts and mathematical structures appearing in the analysis of large quantum
Wladyslaw Adam Majewski
doaj   +1 more source

Quantum stochastic calculus and quantum Gaussian processes [PDF]

Indian Journal of Pure and Applied Mathematics, 2015
In this lecture we present a brief outline of boson Fock space stochastic calculus based on the creation, conservation and annihilation operators of free field theory, as given in the 1984 paper of Hudson and Parthasarathy. We show how a part of this architecture yields Gaussian fields stationary under a group action.
openaire   +3 more sources