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Getting a stochastic process from a conservative Lagrangian: A first approach

Author

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  • Ramírez, J.E.
  • Herrera, J.N.
  • Martínez, M.I.

Abstract

The transition probability PV for a stochastic process generated by a conservative Lagrangian L=L0−εV is obtained at first order from a perturbation series found using a path integral. This PV corresponds to the transition probability for a random walk with a probability density given by the sum of a normal distribution and a perturbation which may be understood as the contribution of the interaction of the random walk with the external field. It is also found that the moment-generating function for PV can be expressed as the generating function of a normal distribution modified by a perturbation. Applications of these results to a linear potential, a harmonic oscillator potential, and an exponentially decaying potential are shown.

Suggested Citation

  • Ramírez, J.E. & Herrera, J.N. & Martínez, M.I., 2016. "Getting a stochastic process from a conservative Lagrangian: A first approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 1-9.
    • Handle: RePEc:eee:phsmap:v:448:y:2016:i:c:p:1-9
    DOI: 10.1016/j.physa.2015.12.067
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    References listed on IDEAS

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    1. Caldeira, A.O. & Leggett, A.J., 1983. "Path integral approach to quantum Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(3), pages 587-616.
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