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Lattice scars: surviving in an open discrete billiard

AuthorsFernández-Hurtado, Victor; Mur-Petit, Jordi ; García-Ripoll, Juan José ; Molina, Rafael A.
Keywordsquantum chaos
cold atoms
optical lattice
open quantum systems
Issue Date6-Jun-2014
AbstractWe 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.
DescriptionEditorially selected as an "IoP Select" article. Part of "Focus on Coherent Control of Complex Quantum Systems". 14 pag, 67 refs, 2 videos.
Publisher version (URL)http://dx.doi.org/10.1088/1367-2630/16/3/035005
Appears in Collections:(CFMAC-IEM) Artículos
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131202-lattice_scars-njp-sent.pdfTexto del artículo2,38 MBAdobe PDFThumbnail
scary_movie-rect_all.aviVideo with time evolution on a rectangular billiard10,33 MBvideo/avi (created with Matlab R2010b)View/Open
scary_movie-bunim_full.aviVideo with time evolution on a Bunimovich stadium billiard3,89 MBvideo/avi (created with Matlab R2010b)View/Open
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