Exponentially FragilePTSymmetry in Lattices with Localized Eigenmodes

Exponentially fragile PT symmetry in lattices with localized eigenmodes.

We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting delta approximately exp(-N/xi) where xi is their localization length. The level "evolution" with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The sp...

Exponentially Localized Solutions of Mel’nikov Equation

The Mel’nikov equation is a (2+1) dimensional nonlinear evolution equation admitting boomeron type solutions. In this paper, after showing that it satisfies the Painlevé property, we obtain exponentially localized dromion type solutions from the bilinearized version which have not been reported so far. We also obtain more general dromion type solutions with spatially varying amplitude as well a...

Localized states on comb lattices.

Complex networks and graphs provide a general description of a great variety of inhomogeneous discrete systems. These range from polymers and biomolecules to complex quantum devices, such as arrays of Josephson junctions, microbridges, and quantum wires. We introduce a technique, based on the analysis of the motion of a random walker, that allows us to determine the density of states of a gener...

Exponentially Localized Wannier Functions in Periodic Zero Flux Magnetic Fields

Localized excitations in two-dimensional Hamiltonian lattices.

We analyze the origin and features of localized excitations in a discrete two-dimensional Hamiltonian lattice. The lattice obeys discrete translational symmetry, and the localized excitations exist because of the presence of nonlinearities. We connect the presence of these excitations with the existence of local integrability of the original N degree of freedom system. On the basis of this expl...