Backward non-unitary quantum evolution

Abstract

A non-linear backward equation with diffusive terms is postulated for the probability density that depends on the Bohmian quantum potential. An associated nonlinear Schrödinger equation is also introduced and extension of the analysis to several particle compounds is sketched along with the implications following from this formalism regarding the non-conservation of probability in the non-equilibrium regime. Some further conclusions are educed with respect to the Onsager's relations and the generalized optical theorem.