Hear $\ddot{I}€$ from Quantum Galperin Billiards

Abstract

Galperin introduced an interesting method to learn the digits of $\ddot{I}€$ by counting the collisions of two billiard balls and a hard wall. This paper studies two quantum versions of the Galperin billiards. It is shown that the digits of $\ddot{I}€$ can be observed in the phase shifts of the quantum models.

published version