Correlated Random Tight-Binding System with One Periodic State: Its Time Evolution and the Effects of an Added Nonlinearity

Abstract

We study a one-dimensional tight-binding system with constant on-site potential and off-diagonal hopping integrals t binary valued, and distributed as correlated random dimers. An explicit transformation from the system with constant t reveals that not only all states are extended, but in addition one of the states is periodic. The transformation is valid also for the corresponding timedependent system, even including a nonlinear term. An example of the time evolution of a solitonlike state is shown.

Renormalization transformation of periodic and aperiodic lattices

“…͑1͒ and ͑5͒, respectively, and U is a unitary diagonal matrix. 32 In this case, the energies of the eigenstates are not affected by the transformation and the elements of the transformation matrix are recursively obtained from the knowledge of the original hopping integrals. 32 Inspired by these previous results, in this work we will introduce a local similarity transformation which can act at two different scale lengths.…”

Delocalization of two interacting particles in a random potential: One-dimensional electric interaction

“…The role of internal spatial local correlations at the random potential has been considered as mechanism of delocalization. In fact, there is theoretical [6][7][8][9][10][11][12][13][14][15][16][17][18][19] and experimental [20] evidence of delocalization due to correlations. Moreover, the role of no local correlation has been studied showing new phenomena of delocalization [21].…”

“…Namely, if ξ(x) = f i (x−x i ) then every function f i is independent (also the random variable x i ). So, if there are extended states they are not related to correlations at the random potential [6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”