Stochastic Dynamics and the Semiclassical Limit of Quantum Mechanics

  • G. Jona-Lasinio


We outline a new approach to tunnelling problems in quantum mechanics based on the so called stochastic quantization. The starting point of the method is the Observation that in the limit \(\frac{\hbar }{m} \to o\)one can approximate the stochastic process underlying the quantum motion with a Markov chain making transitions at random times from one classical equilibrium position to another. This picture is suggested by the theory of small random perturbations of dynamical systems developed by Ventzel and Freidlin which provides the natural mathematical ideas for our purpose.

As an example of application we discuss the instanton problem for the double well anharmonic oscillator. The flexibility and wide applicability of the present approach is pointed out.


Semiclassical Limit Anharmonic Oscillator Drift Term Stochastic Quantization Strong Markov Property 
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Copyright information

© Springer-Verlag/Wien 1980

Authors and Affiliations

  • G. Jona-Lasinio
    • 1
  1. 1.Istituto di Fisica dell’, Gruppo G.N.S.MUniversità — RomaRomaItaly

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