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Stochastic Path-Integral Analysis of the Continuously Monitored Quantum Harmonic Oscillator
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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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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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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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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Connecting Two Stochastic Theories That Lead to Quantum Mechanics
Frontiers in Physics, 2020 The connection is established between two theories that have developed independently with the aim to describe quantum mechanics as a stochastic process, namely stochastic quantum mechanics (sqm) and stochastic electrodynamics (sed).
Luis de la Peña +2 more
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Classical and quantum stochastic thermodynamics [PDF]
Revista Brasileira de Ensino de Física, 2020 The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a stochastic dynamics ...
Mário J. de Oliveira
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Time evolution with symmetric stochastic action
Physical Review Research, 2021 The time evolution of quantum fields is shown to be equivalent to a time-symmetric Fokker-Planck equation. Results are obtained using a Q-function representation, including fermion-fermion, boson-boson, and fermion-boson interactions with linear ...
Peter D. Drummond
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Time-Slicing Path-integral in Curved Space [PDF]
Quantum, 2022 Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them covariant with ...
Mingnan Ding, Xiangjun Xing
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