Friday, May 24, 2013

1305.5370 (Víctor Fernández-Hurtado et al.)

Quantum chaos in open discrete systems: Lattice scars at the band center    [PDF]

Víctor Fernández-Hurtado, Jordi Mur-Petit, Juan José García-Ripoll, Rafael A. Molina
We study the eigenvalues and eigenfunctions of systems on a discrete bounded lattice (lattice billiards). The statistical properties of the spectra show universal features related to the regular or chaotic properties of the dynamics of their classical continuum counterparts. However, the decay dynamics of the open systems appear very different from the continuum case, its 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 E=0, the center of the band. We prove that their existence is intimately related to the discrete and bipartite nature of the underlying lattice, and give a formula to determine their number. Finally, we discuss how to observe lattice scars using cold atoms in optical lattices, photonic waveguides, and quantum circuits.
View original:

No comments:

Post a Comment