Quantum Revivals of Morse Oscillators and Farey-Ford Geometry

TL;DR

This paper investigates quantum revivals in Morse oscillators using analytical solutions, revealing how anharmonicity influences revival times and employing Farey-Ford geometry for fractional revival analysis, with potential applications in spectroscopy and quantum computing.

Contribution

It introduces a novel application of Farey-Ford geometry to analyze fractional quantum revivals in Morse oscillators, linking semi-classical and quantum revival times through number theory.

Findings

Morse anharmonicity affects revival times.

Farey-Ford geometry effectively visualizes fractional revivals.

Quantum deviation parameter relates quantum and semi-classical revival times.

Abstract

Analytical eigensolutions for Morse oscillators are used to investigate quantum resonance and revivals and show how Morse anharmonicity affects revival times. A minimum semi-classical Morse revival time Tmin-rev found by Heller is related to a complete quantum revival time Trev using a quantum deviation parameter that in turn relates Trev to the maximum quantum beat period Tmax-beat. Also, number theory of Farey and Thales-circle geometry of Ford is shown to elegantly analyze and display fractional revivals. Such quantum dynamical analysis may have applications for spectroscopy or quantum information processing and computing.