Pré-Publication, Document De Travail Année : 2020

Growth of the Wang-Casati-Prosen counter in an integrable billiard

Résumé

This work is motivated by an article by Wang, Casati, and Prosen [Phys. Rev. E, 89:042918, 2014] devoted to a study of ergodicity in two-dimensional irrational right-triangular billiards. Numerical results presented there suggest that the irrational contribution to the velocity orientation remains localized as the system evolves, hence pointing to an absence of ergodicity. We study an analogue of the Wang-Casati-Prosen counter for a 45:45:90 degree billiard---a manifestly non-ergodic system with only eight velocity orientations for any generic trajectory---and find no localization even there. What we found instead is an extremely slow, logarithmic growth that could be hard to detect numerically.

Dates et versions

hal-03079802 , version 1 (17-12-2020)

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Zaijong Hwang, Christoph A. Marx, Joseph Seaward, Svetlana Jitomirskaya, Maxim Olshanii. Growth of the Wang-Casati-Prosen counter in an integrable billiard. 2020. ⟨hal-03079802⟩
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