Schrodinger-Newton equation with complex Newton constant and induced gravity

TL;DR

This paper introduces a modified Schrödinger-Newton equation with a complex Newton constant, leading to irreversible dynamics and induced gravity effects, verified through numerical simulations and two-body analysis.

Contribution

It proposes a novel complex Newton coupling in the Schrödinger-Newton equation, resulting in irreversible behavior and induced gravity phenomena.

Findings

Initial states converge to solitonic stationary states.

Effective gravity is induced by imaginary mean-fields.

Induced gravity strength depends on local wave functions.

Abstract

In the reversible Schrodinger-Newton equation a complex Newton coupling G*exp(-i*alpha) 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.