Billiards and toy gravitons

DOI10.1007/S10955-019-02252-0zbMATH Open1447.82020arXiv1808.10547OpenAlexW3100733442WikidataQ128335137 ScholiaQ128335137MaRDI QIDQ2000719

Alfonso Artigue

Publication date: 28 June 2019

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Abstract: In this article we study the one-dimensional dynamics of elastic collisions of particles with positive and negative mass. We show that such systems are equivalent to billiards induced by an inner product of possibly indefinite signature, we characterize the systems with finitely many collisions and we prove that a small particle of negative mass between two particles of positive mass acts like an attracting particle with discrete acceleration (at the collisions) provided that the total kinetic energy is negative. In the limit of the negative mass going to zero, with fixed negative kinetic energy, we obtain a continuous acceleration with potential energy of the form $U(r)=-k/r^2$.

Full work available at URL: https://arxiv.org/abs/1808.10547

zbMATH Keywords

negative massbilliardelastic collision

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Collisions in celestial mechanics, regularization (70F16) Dynamical systems with singularities (billiards, etc.) (37C83)

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