Lattice scars: Surviving in an open discrete billiard
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.
Cite
@article{arxiv.1305.5370,
title = {Lattice scars: Surviving in an open discrete billiard},
author = {Víctor Fernández-Hurtado and Jordi Mur-Petit and Juan José García-Ripoll and Rafael A. Molina},
journal= {arXiv preprint arXiv:1305.5370},
year = {2014}
}
Comments
14 one-column pages, 6 figures. Watch appearance of scars during dynamical evolution on movies at http://www.youtube.com/watch?v=1sCbQmYfF-E and http://www.youtube.com/watch?v=3XZw4zZjrG0. v2: title changed; more details on experimental implementations. Accepted for publication by New J. Phys