Finite dimensional systems with random external fields and neutrino propagation in fluctuating media

Abstract

We develop the general formalism for the study of neutrino propagation in presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival probabilities and higher order distribution moments. The formalism applies equally to any finite dimensional Schroedinger equation in presence of a stochastic external force. New integro-differential equations valid for finite correlated processes are obtained for the first time. For the particular case of exponentially correlated processes a second order ordinary equation is obtained. As a consequence, the Redfield equation valid for Gaussian delta-correlated noise is rederived in a simple way. The formalism, together with the quantum correlation theorem is applied to the computation of higher moments and correlation functions of practical interest in forthcoming high precision neutrino experiments. It is shown that equal and not equal time correlators follow similar differential equations.