Quantum chaos of dark matter in the Solar System

TL;DR

This paper investigates the quantum chaotic behavior of dark matter particles in the Solar System, revealing significant quantum effects at extremely small mass ratios and drawing parallels with atomic ionization phenomena.

Contribution

It introduces a quantum dynamical model for dark matter in the Solar System and identifies the conditions under which quantum effects become prominent, including localization phenomena.

Findings

Quantum effects become significant for dark matter mass ratio below 2×10^{-15}.

Dark matter exhibits exponential localization analogous to Anderson localization.

Lifetime of dark matter in the Solar System depends on mass ratio and localization regime.

Abstract

We perform time-dependent analysis of quantum dynamics of dark matter particles in the Solar System. It is shown that this problem has similarities with a microwave ionization of Rydberg atoms studied previously experimentally and analytically. On this basis it is shown that the quantum effects for chaotic dark matter dynamics become significant for dark matter mass ratio to electron mass being smaller than $2 \times 10^{-15}$. Below this border multiphoton diffusion over Rydberg states of dark matter atom becomes exponentially localized in analogy with the Anderson localization in disordered solids. The life time of dark matter in the Solar System is determined in dependence on mass ratio in the localized phase and a few photon ionization regime. The quantum effects for dark matter captured by other binary systems are also discussed.