Localization transition in incommensurate non-Hermitian systems.
A class of one-dimensional lattice models with an incommensurate complex potential V(theta)=2[lambda(r) cos(theta)+i(lambda)(i) sin(theta)] is found to exhibit a localization transition at /lambda(r)/+/lambda(i)/=1. This transition from extended to localized states manifests itself in the behavior of the complex eigenspectum. In the extended phase, states with real eigenenergies have a finite measure, and this measure goes to zero in the localized phase. Furthermore, all extended states exhibit real spectra provided /lambda(r)/>or=/lambda(i)/. Another interesting feature of the system is the fact that the imaginary part of the spectrum is sensitive to the boundary conditions only at the onset to localization.
Jazaeri
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Department of Physics and School of Computational Sciences, George Mason University, Fairfax, Virginia 22030, USA.
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