Lattice scars: Surviving in an open discrete billiard

TL;DR

This paper introduces 'lattice scars', special states in open quantum lattice systems that persist indefinitely, revealing unique decay dynamics and potential applications in quantum transport across various platforms.

Contribution

It identifies and analytically characterizes a new class of states called lattice scars that survive in dissipative quantum lattice systems, expanding understanding of quantum decay processes.

Findings

Lattice scars are degenerate at the band center and persist indefinitely.

Analytical formula for the number of lattice scars in bipartite lattices.

Potential observation methods include photonic waveguides and cold atom systems.

Abstract

We study quantum systems on a discrete bounded lattice (lattice billiards). The statistical properties of their spectra show universal features related to the regular or chaotic character of their classical continuum counterparts. However, the decay dynamics of the open systems appear very different from the continuum case, their properties being dominated by the states in the band center. We identify a class of states ("lattice scars") that survive for infinite times in dissipative systems and that are degenerate at the center of the band. We provide analytical arguments for their existence in any bipartite lattice, and give a formula to determine their number. These states should be relevant to quantum transport in discrete systems, and we discuss how to observe them using photonic waveguides, cold atoms in optical lattices, and quantum circuits.