L. Garrido

Response and Correlation in Fokker-Planck Dynamics. I

The perturbative expansion of the correlation and response functions in Fokker-Planck dynamics is carried out through a Wicks theorem for a general non-stationary situation. The stochastic force is introduced dynamically by means of noncommuting variables and the equivalence of Langevin dynamics and Fokker-Planck dynamics in the Heisenberg picture is explicitly proved. No restriction is imposed on the initial value distribution, so that initial non-Gaussian correlations are considered. It is concluded that the whole effect of the stochastic force is the appearance of a stochastic propagator that dresses the free correlation function. Wylds equation for the turbulence problem is derived.

Stochastic Quantization and Detailed Balance in Fokker-Planck Dynamics

The path integral and operator formulations of the Fokker-Planck equation are considered as stochastic quantizations of underlying Euler-Lagrange equations. The operator formalism is derived from the path integral formalism. It is proved that the Euler-Lagrange equations are invariant under time reversal if detailed balance holds and it is shown that the irreversible behavior is introduced through the stochastic quantization. To obtain these results for the nonconstant diffusion Fokker-Planck equation, a transformation is introduced to reduce it to a constant diffusion Fokker-Planck equation. Critical comments are made on the stochastic formulation of quantum mechanics.

General transformations from multiplicative noise to additive noise

Abstract General transformations from multiplicative noise to additive noise are obtained for systems whose dynamical evolution is given by multidimensional Langevin equations.

Approximate Constancy of Adiabatic Invariants in Plasma Physics

The interaction representation for classical mechanics starting from an operational formulation of the same is presented. General criteria to be satisfied by a slowly time-dependent Hamiltonian in order to possess adiabatic invariants of the m-th order are given. A general method, based on techniques similar to those used to evaluate timedependent perturbations in quantum mechanics, to calculate the degree of approximate constancy of such adiabatic invariants for Hamiltonians depending slowly but at a finite rate on time is discussed. These methods were applied to the adiabatic invariants that appear in thermonuclear plasma, evaluating the errors made in the guiding center approximation. (auth)

Geometrical derivation of the intrinsic Fokker-Planck equation and its stationary distribution

Starting from an intrinsic Langevin equation, we give a geometrical derivation of the Fokker-Planck equation. We also present a method for obtaining a stationary distribution and for deriving potential conditions when the diffusion matrix is singular.

Stochastic quantization and path integral formulation of Fokker-Planck equation

Abstract The operator formalism (Fokker-Planck dynamics) associated to a general n -dimensional, non-linear drift, non-constant diffusion Fokker-Planck equation, is derived by a stochastic quantization from the corresponding path integral formulation in phase space.

Sufficient intrinsic conditions for the existence of a non-equilibrium phase transition

Abstract In this letter we present sufficient intrinsic condition for the existence of a non-equilibrium phase transition. This paper is a progress report of a work that tries to find sufficient and necessary conditionsins order that a non-equilibrium phase transition takes place.