Instabilidade modulacional e auto-armadilhamento em cadeias com interação de longo alcance entre íons

Abstract

In this work we investigate the modulational instability (MI) of a electronic wave function near to steady state in a discrete one-dimensional lattice where take into account a long-hopping kinetic term. This hopping term decays with the distance between points of the chain under power law as | i − j| −α characterized by α exponent modulating this interaction. The numerical results show that for large α reproduce the short-range hopping (first neighbors) case. In this specific case the characteristic critical parameter χMI of MI, above which the wave solution becomes unstable, scales linearly as the inverse of the size L of chain. In range 2 < α < 10 the electronic probability density remains to be stable, because χMI becomes larger as the exponent α decreases. Observed that for α = 2, the size L of the chain doesn’t influence in instability of the electronic wave function. This result, characteristic of two-dimensional systems, corroborates whit analytical analysis of effective dimensinality of the system. In the last range, 1 < α < 2, a transition that occurs in the behavior of the parameter critical χMI relative to the size of the chain, that now grows with increasing L. Therefore the electronic wave packet remains stable except for large values to effective coupling of non-linearity. Besides that, we mapped to several values of the hopping exponent where the wave function presents the extended character, breathers, chaotic dynamics as well as self-trapping state of localization. An effective dimensionality analysis of the modulational instability of the CW state of the system showed that stability occurs α 6 3 with χIM ∝ N2−α. The instability regime emerges for α > 3 with χIM ∝ N −1. The numerical results obtained corroborated this analytical analysis of the spectral dimensionality of the system.