Path Integral approach to kinematical browmian motion, due to random canonical transformation

Details Path Integral approach to kinematical browmian motion, due to random canonical transformation Path Integral approach to kinematical browmian motion, due to random canonical transformation

2006-04-21

arxiv.org/abs/nlin/0604051v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, no figure

Scientific paper

The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian quantum theory is obtained. The conditional transition probability density of the presence of a Browmian particle is obtained with the help of the functional integral. The technique of factorisation of the solution of the Fokker-Planck equation is employed to evaluate the effective potential energy.

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