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.

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

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Cited by in corpus (10)

• Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries
• Chiral bound states in the continuum
• Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices
• Quantum probe spectroscopy for cold atomic systems
• Disorder enhanced quantum many-body scars in Hilbert crystals
• Variational Scarring in Graphene Quantum Dots
• Van Hove bound states in the continuum: Localised subradiant states in finite open lattices
• Exceptional stationary state in a dephasing many-body open quantum system
• Dynamics of two-dimensional open quantum lattice models with tensor networks
• The simplest 2D quantum walk detects chaoticity