PROPERTIES OF NONLINEAR SCHRODINGER-EQUATIONS ASSOCIATED WITH DIFFEOMORPHISM GROUP-REPRESENTATIONS

The authors recently derived a family of nonlinear Schrodinger equatio ns on R3 from fundamental considerations of generalized symmetry: ihBA Rpartial derivative(t)psi = -(hBAR2/2m)del2psi + F[psi, psiBAR]psi + i hBAR{del2psi + (\delpsi\2/\psi\2)psi}, where F is an arbitrary real fu nctional and D a real, continuous quantum number. These equations, des criptive of a quantum mechanical current that includes a diffusive ter m, correspond to unitary representations of the group Diff (M) paramet rized by D, where M = R3 is the physical space. In the present paper w e explore the most natural ansatz for F, which is labelled by five rea l coefficients. We discuss the invariance properties, describe the sta tionary states and some non-stationary solutions, and determine the ex tra, dissipative terms that occur in the Ehrenfest theorem. We identif y an interesting, Galilean-invariant subfamily whose properties we inv estigate, including the case where the dissipative terms vanish.