Newtonian Self-Gravitation in the Neutral Meson System

Abstract

We derive the effect of the Schrödinger--Newton equation, which can be considered as a non-relativistic limit of classical gravity, for a composite quantum system in the regime of high energies. Such meson-antimeson systems exhibit very unique properties, e.g. distinct masses due to strong and electroweak interactions. We find conceptually different physical scenarios due to lacking of a clear physical guiding principle which mass is the relevant one and due to the fact that it is not clear how the flavor wave-function relates to the spatial wave-function. There seems to be no principal contradiction. However, a nonlinear extension of the Schrödinger equation in this manner strongly depends on the relation between the flavor wave-function and spatial wave-function and its particular shape. In opposition to the Continuous Spontaneous Localization collapse models we find a change in the oscillating behavior and not in the damping of the flavor oscillation.

arXiv comment10 pages, no figures

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• Particle mixing and the emergence of classicality: A spontaneous-collapse-model view
• The effects of the dark energy on the static Schrödinger-Newton system -- an Adomian Decomposition Method and Padé approximants based approach
• Series solution of the time-dependent Schrödinger-Newton equations in the presence of dark energy via the Adomian Decomposition Method