A Schrodinger-like probability amplitude description of an ensemble of a class of Hamiltonian dynamical systems and the concept of ensemble modes

Abstract

It is pointed out that the behaviour of certain appropriate ensembles of a class of Hamiltonian systems can be described in terms of a set of probability amplitudes obeying Schrodinger like equations. Such a description leads to a new concept of "ensemble modes" described by the different equations. Such "ensemble modes" have in fact been observed experimentally recently in a certain classical mechanical system and thus testify to the validity of the probability amplitude description for the classical deterministic system. The possibility of the existence of new modes of quantum behaviour corresponding to the new ensemble modes other than the Schrodinger mode is also pointed out.