Quantum carpets from Gaussian sum theory

TL;DR

This paper introduces a unified analytical framework using Gaussian sum theory to explain the formation of quantum carpets, including revivals and diagonal canals, enhancing understanding of their interference patterns.

Contribution

It presents a complete formula for fractional revival generation and explores the geometric interpretation of interference in diagonal canals, advancing quantum carpet analysis.

Findings

Derived a formula explaining fractional revival via Gaussian sum theory

Revealed geometric relations of interference terms in diagonal canals

Enhanced understanding of quantum carpet formation mechanisms

Abstract

In many closed quantum systems, an interesting phenomenon, called quantum carpet, can be observed, where the evolution of wave function exhibits a carpet-like pattern. The mechanism of quantum carpet is similar to the classical interference pattern of light. Although the origin of quantum carpets has been studied previously, there are still many interesting details worth exploring. Here, we presented a unified framework for a simultaneous analyzing on three features of quantum carpets, namely full revival, fractional revival and diagonal canal. For fractional revival, a complete formula is presented to explain its generation through "Gaussian sum theory", in which all the essential features, including the phases and amplitudes, of this phenomenon could be captured analytically. Moreover, we also revealed the relations between the interference terms of the diagonal canals and their geometric interpretations, providing a better understanding in the formation of diagonal canals.