The Monte Carlo wave-function method: A robust adaptive algorithm and a study in convergence

M. Kornyik, A. Vukics

Research output: Article

Abstract

We present a stepwise adaptive-timestep version of the Quantum Jump (Monte Carlo wave-function) algorithm. Our method has proved to remain robust even for problems where the integrating implementation of the Quantum Jump method is numerically problematic. The only specific parameter of our algorithm is the single a priory parameter of the Quantum Jump method, the maximal allowed total jump probability per timestep. We study the convergence of ensembles of trajectories to the solution of the full master equation as a function of this parameter. This study is expected to pertain to any possible implementation of the Quantum Jump method.

Original languageEnglish
JournalComputer Physics Communications
DOIs
Publication statusAccepted/In press - jan. 1 2019

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Wave functions
Adaptive algorithms
wave functions
Trajectories
trajectories

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)

Cite this

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abstract = "We present a stepwise adaptive-timestep version of the Quantum Jump (Monte Carlo wave-function) algorithm. Our method has proved to remain robust even for problems where the integrating implementation of the Quantum Jump method is numerically problematic. The only specific parameter of our algorithm is the single a priory parameter of the Quantum Jump method, the maximal allowed total jump probability per timestep. We study the convergence of ensembles of trajectories to the solution of the full master equation as a function of this parameter. This study is expected to pertain to any possible implementation of the Quantum Jump method.",
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author = "M. Kornyik and A. Vukics",
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AB - We present a stepwise adaptive-timestep version of the Quantum Jump (Monte Carlo wave-function) algorithm. Our method has proved to remain robust even for problems where the integrating implementation of the Quantum Jump method is numerically problematic. The only specific parameter of our algorithm is the single a priory parameter of the Quantum Jump method, the maximal allowed total jump probability per timestep. We study the convergence of ensembles of trajectories to the solution of the full master equation as a function of this parameter. This study is expected to pertain to any possible implementation of the Quantum Jump method.

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KW - Markov approximation

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KW - Open quantum systems

KW - Quantum jumps

KW - Stochastic simulations

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