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.

10 pages, no figures

References in corpus (4)

• The Schrödinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
• Centre-of-mass motion in multi-particle Schroedinger-Newton dynamics
• Intrinsic CPT violation and decoherence for entangled neutral mesons
• The frictional Schrödinger-Newton equation in models of wave function collapse

Cited by in corpus (3)

• 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