Quantum chaos of dark matter in the Solar System

Dima Shepelyansky (1)

1 ICQ - Cohérence Quantique (LPT)

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 × 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. Various implications of these quantum results are discussed for the capture of dark matter from Galaxy and its steady-state density distribution. PACS numbers: 95.35.+d, 32.80.Rm, 05.45.Mt, 95.10.Fh Introduction.– The properties of dark matter are now actively discussed by the astronomy community (see e.g. [1]). Recently, a necessity of correct description of galac-tic structures, in particularly singular density cusp problem , attracted a growing interest to the ultralight dark matter particles (DMP) of bosons with a mass m d ∼ 10 −22 eV (see e.g. [2–5] and Refs. therein). However, the mass m d of light DMP is unknown and possibilities of its detection are under active discussions [2, 6]. At small values of m d (or its ratios to electron mass m e) the quantum effects start to be dominant [4, 5, 7]. Till present the quantum effects have been studied in the frame of static solutions of Schrödiner and Poisson equations.

Domaines: Planétologie et astrophysique de la terre [astro-ph.EP]; Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]; Physique Atomique [physics.atom-ph]; Dynamique Chaotique [nlin.CD]

Dima Shepelyansky. Quantum chaos of dark matter in the Solar System. 2017. ⟨hal-01643068⟩