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Quantum Stochastic Calculus and Quantum Gaussian Processes [PDF]
Indian Journal of Pure and Applied Mathematics, 2014 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.
Parthasarathy, K. R.
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A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus [PDF]
EntropyWe 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
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Two-particle quantum correlations in stochastically-coupled networks [PDF]
New Journal of Physics, 2019 Quantum walks in dynamically-disordered networks have become an invaluable tool for understanding the physics of open quantum systems. Although much work has been carried out considering networks affected by diagonal disorder, it is of fundamental ...
Roberto de J León-Montiel +6 more
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Photoemissive sources and quantum stochastic calculus [PDF]
Banach Center Publications, 1997 Just at the beginning of quantum stochastic calculus Hudson and Parthasarathy proposed a quantum stochastic Schrodinger equation linked to dilations of quantum dynamical semigroups.
Barchielli, Alberto, Lupieri, Giancarlo
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Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2000 A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space $\eufrak{h}$ and it is shown that they satisfy similar properties as the ...
Belavkin V. P. +3 more
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A Stochastic Fractional Calculus with Applications to Variational Principles
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
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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.
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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
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A Nonlocal Approach to The Quantum Kolmogorov Backward Equation and Links to Noncommutative Geometry [PDF]
, 2019 The Accardi-Boukas quantum Black-Scholes equation can be used as an alternative to the classical approach to finance, and has been found to have a number of useful benefits.
Hicks, Will
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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
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