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Stochastic integral representation theorem for quantum semimartingales
Journal of Functional Analysis, 2003 The quantum stochastic integral of Itô type formulated by \textit{R. L. Hudson} and \textit{K. R. Parthasarathy} [Commun. Math. Phys. 93, 301--323 (1984; Zbl 0546.60058)] is extended to a wide class of adapted quantum stochastic processes on Boson Fock space.
Un Çig Ji
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Stochastic Path-Integral Analysis of the Continuously Monitored Quantum Harmonic Oscillator [PDF]
PRX Quantum, 2022 We consider the evolution of a quantum simple harmonic oscillator in a general Gaussian state under simultaneous time-continuous weak position and momentum measurements.
Tathagata Karmakar +2 more
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Motion of Quantum Particles in Terms of Probabilities of Paths [PDF]
EntropyThe Feynman path integral formalism for non-relativistic quantum mechanics is revisited. A comparison is made with cases of light propagation (Huygens’ principle) and Brownian motion. The difficulties for a physical model applying Feynman’s formalism are
Emilio Santos
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The Stochastic-Quantum Correspondence [PDF]
Philosophy of PhysicsThis paper argues that every quantum system can be understood as a sufficiently general kind of stochastic process unfolding in an old-fashioned configuration space according to ordinary notions of probability.
Jacob A. Barandes
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Stochastic analysis & discrete quantum systems
Nuclear Physics B, 2019 We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the Cameron-Martin-Girsanov theorem.
Anastasia Doikou +2 more
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Stochastic path-integral formalism for continuous quantum measurement
Physical Review A, 2015 We generalize and extend the stochastic path integral formalism and action principle for continuous quantum measurement introduced in [A. Chantasri, J. Dressel and A. N. Jordan, Phys. Rev. A {\bf 88}, 042110 (2013)], where the optimal dynamics, such as the most-likely paths, are obtained by extremizing the action of the path integral.
Chantasri, Areeya, Jordan, Andrew N.
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Quantum stochastic integrals under standing hypotheses
Journal of Mathematical Analysis and Applications, 1987 We study the meaning of stochastic integrals when the integrator is a quantum stochastic process which is not quite a martingale, in that it obeys estimates of the type advocated by \textit{E. J. McShane} [Stochastic calculus and stochastic models. (1974; Zbl 0292.60090)] in the classical case.
Barnett, C, Streater, R.F, Wilde, I.F
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Quantum stochastic integrals as belated integrals [PDF]
Glasgow Mathematical Journal, 1992 Quantum stochastic integrals have been constructed in various contexts [2, 3, 4, 5, 9] by adapting the construction of the classical L2-Itô-integral with respect to Brownian motion. Thus, the integral is first defined for simple integrands as a finite sum, then one establishes certain isometry relations or suitable bounds to allow the extension, by ...
Barnett, Chris +2 more
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Risenologi, 2020 The implementation of Lévy path integral generated by Lévy stochastic process on fractional Schrödinger equation has been investigated in the framework of fractional quantum mechanics.
Chandra Halim, M. Farchani Rosyid
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New Journal of Physics, 2022 Here we present a novel stochastic Liouville equation with piecewisely correlated noises, in which the inter-piece correlation is rigorously incorporated by a convolution integral involving functional derivatives.
Yun-An Yan, Xiao Zheng, Jiushu Shao
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