Periodic wave packet reconstruction in truncated tight-binding lattices

TL;DR

This paper explores wave packet reconstruction in truncated tight-binding lattices, demonstrating periodic dynamics such as Bloch oscillations and self-imaging in both Hermitian and non-Hermitian systems with specific energy level structures.

Contribution

It introduces a class of truncated tight-binding lattices with commensurate energy levels that exhibit periodic wave packet reconstruction, including novel non-Hermitian cases.

Findings

Demonstrates exact Bloch oscillations in finite lattices

Shows periodic wave packet dynamics in non-Hermitian lattices

Achieves self-imaging in lattices with quadratically-varying energy levels

Abstract

A class of truncated tight-binding Hermitian and non-Hermitian lattices with commensurate energy levels, showing periodic reconstruction of the wave packet, is presented. Examples include exact Bloch oscillations on a finite lattice, periodic wave packet dynamics in non-Hermtian lattices with a complex linear site-energy gradient, and self-imaging in lattices with commensurate energy levels quadratically-varying with the quantum number.