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Path probability distribution of stochastic motion of non dissipative systems: a classical analog of Feynman factor of path integral

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  • Lin, T.L.
  • Wang, R.
  • Bi, W.P.
  • El Kaabouchi, A.
  • Pujos, C.
  • Calvayrac, F.
  • Wang, Q.A.

Abstract

We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model of simulation is a one-dimensional particle subject to conservative force and Gaussian random displacement. The probability that a sample path between two fixed points is taken is computed from the number of particles moving along this path, an output of the simulation, divided by the total number of particles arriving at the final point. It is found that the path probability decays exponentially with increasing action of the sample paths. The decay rate increases with decreasing randomness. This result supports the existence of a classical analog of the Feynman factor in the path integral formulation of quantum mechanics for Hamiltonian systems.

Suggested Citation

  • Lin, T.L. & Wang, R. & Bi, W.P. & El Kaabouchi, A. & Pujos, C. & Calvayrac, F. & Wang, Q.A., 2013. "Path probability distribution of stochastic motion of non dissipative systems: a classical analog of Feynman factor of path integral," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 129-136.
    • Handle: RePEc:eee:chsofr:v:57:y:2013:i:c:p:129-136
    DOI: 10.1016/j.chaos.2013.10.002
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    References listed on IDEAS

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    1. Wang, Q.A. & Bangoup, S. & Dzangue, F. & Jeatsa, A. & Tsobnang, F. & Le Méhauté, A., 2009. "Reformulation of a stochastic action principle for irregular dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2550-2556.
    2. Wang, Qiuping A., 2005. "Non-quantum uncertainty relations of stochastic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1045-1052.
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