NONLINEAR SCHRODINGER-EQUATIONS AND THE SEPARATION PROPERTY

Hierarchies of nonlinear Schrodinger equations were investigated for m ultiparticle systems, satisfying the separation property, i.e., where product wave functions evolve by the separate evolution of each factor . Such a hierarchy defines a nonlinear derivation on tensor products o f the single-particle wave-function space, and satisfies a certain hom ogeneity property characterized by two new universal physical constant s. A canonical construction of hierarchies is derived that allows the introduction, at any particular ''threshold'' number of particles, of truly new physical effects absent in systems having fewer particles. I n particular, if single quantum particles satisfy the usual (linear) S chrodinger equation, a system of two particles can evolve by means of a fairly simple nonlinear Schrodinger equation without violating the s eparation property. Examples of Galilean-invariant hierarchies are giv en.