Schrödinger–Newton equation with a complex Newton constant and induced gravity

In the reversible Schrödinger–Newton equation a complex Newton coupling Gexp(−iα)Gexp(−iα) is proposed in place of G. The equation becomes irreversible and all initial one-body states are expected to converge to solitonic stationary states. This feature is verified numerically. For two-body solutions we point out that an effective Newtonian interaction is induced by the imaginary mean-fields as if they were real. The effective strength of such induced gravity depends on the local wave functions of the participating distant bodies.