dorsal/arxiv
View SchemaNumerical Implementation of Non-Markovian Quantum State Diffusion
| Authors | Joshua Wilkie, Ray Ng |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510171 |
| URL | https://arxiv.org/abs/quant-ph/0510171 |
Abstract
Non-Markovian quantum state diffusion (NMQSD) is a non-relativistic but otherwise exact theory which expresses the reduced density matrix of an arbitrary subsystem, interacting linearly with an uncoupled harmonic oscillator bath, as an average of diadics formed from state vectors which obey stochastic variational-differential equations. The vacuum radiation field can be represented as such an oscillator bath, and so this model is in widespread use in quantum optics. Prior to the development of NMQSD, exact subsystem solutions could only be obtained in a few special cases (e.g. spin-1/2, harmonic oscillator). Unfortunately, it has not yet been possible to obtain exact solutions to new problems using NMQSD due to the difficulty of solving the variational-differential equations. Here we show that these equations can be transformed into a pair of coupled nonlinear integrodifferential equations. We develop exact numerical methods for the integrodifferential equations and show that solutions can be readily obtained to good accuracy for quite general subsystems. We exactly solve various examples including tunneling in a double well representing molecular isomerization or racemization, suppression of fluorescence from a two-level atom in a band gap, and intermittent fluorescence from a driven three level system representing electronic states of singly ionized magnesium.
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"abstract": "Non-Markovian quantum state diffusion (NMQSD) is a non-relativistic but\notherwise exact theory which expresses the reduced density matrix of an\narbitrary subsystem, interacting linearly with an uncoupled harmonic oscillator\nbath, as an average of diadics formed from state vectors which obey stochastic\nvariational-differential equations. The vacuum radiation field can be\nrepresented as such an oscillator bath, and so this model is in widespread use\nin quantum optics. Prior to the development of NMQSD, exact subsystem solutions\ncould only be obtained in a few special cases (e.g. spin-1/2, harmonic\noscillator). Unfortunately, it has not yet been possible to obtain exact\nsolutions to new problems using NMQSD due to the difficulty of solving the\nvariational-differential equations. Here we show that these equations can be\ntransformed into a pair of coupled nonlinear integrodifferential equations. We\ndevelop exact numerical methods for the integrodifferential equations and show\nthat solutions can be readily obtained to good accuracy for quite general\nsubsystems. We exactly solve various examples including tunneling in a double\nwell representing molecular isomerization or racemization, suppression of\nfluorescence from a two-level atom in a band gap, and intermittent fluorescence\nfrom a driven three level system representing electronic states of singly\nionized magnesium.",
"arxiv_id": "quant-ph/0510171",
"authors": [
"Joshua Wilkie",
"Ray Ng"
],
"categories": [
"quant-ph"
],
"title": "Numerical Implementation of Non-Markovian Quantum State Diffusion",
"url": "https://arxiv.org/abs/quant-ph/0510171"
},
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