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Modeling quantum measurement probability as a classical stochastic process.

Daniel T. Gillespie1, William O. Alltop, Jorge M. Martin

  • 1Research Department, Mail Code 4T4100D, Naval Air Warfare Center, China Lake, California 93555.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
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This study explores non-Markovian processes for modeling quantum oscillator measurements. While several models fit the data, none are fundamentally quantum or describe other oscillator properties.

Area of Science:

  • Quantum Mechanics
  • Statistical Physics
  • Stochastic Processes

Background:

  • Classical stochastic processes can model quantum systems.
  • Markov processes are insufficient for describing quantum oscillator measurement probabilities.
  • Generalizing Markovian equations to non-Markovian ones is complex.

Purpose of the Study:

  • To generalize Markovian Chapman-Kolmogorov and master equations to non-Markovian processes.
  • To apply these generalizations to model a two-state quantum oscillator.
  • To investigate the validity of different non-Markovian models for quantum dynamics.

Main Methods:

  • Described non-Markovian generalizations of Chapman-Kolmogorov and master equations.
  • Devised two novel non-Markovian processes for the two-state quantum oscillator.

Related Experiment Videos

  • Analyzed a previously proposed third non-Markovian modeling process.
  • Performed numerical simulations of the developed processes.

    • Main Results:

    • Successfully modeled the measurement statistics of the two-state quantum oscillator using non-Markovian processes.
    • Identified and clarified three distinct non-Markovian modeling approaches.
    • Numerical simulations demonstrated the behavior of these models.

    Conclusions:

    • Non-Markovian processes can accurately model quantum oscillator measurement statistics.
    • No single non-Markovian model is definitively "quantum" or universally descriptive.
    • These models do not capture the dynamics of non-commuting quantum observables.