Hear $\pi$ from Quantum Galperin Billiards

TL;DR

This paper explores quantum analogs of Galperin billiards, demonstrating that the digits of π can be inferred from phase shifts in these quantum models, extending classical collision-based methods into quantum physics.

Contribution

It introduces two quantum versions of Galperin billiards and shows how π's digits can be extracted from their phase shifts, a novel quantum approach.

Findings

Digits of π observed in quantum phase shifts

Quantum models extend classical collision methods

New quantum techniques for π approximation

Abstract

Galperin introduced an interesting method to learn the digits of $\pi $ 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 $\pi $ can be observed in the phase shifts of the quantum models.