PMID: 11308756Apr 20, 2001Paper

Localization transition in incommensurate non-Hermitian systems

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
A Jazaeri, Indubala I Satija

Abstract

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.

References

Aug 1, 1993·Physical Review. B, Condensed Matter·I I Satija
Oct 2, 1995·Physical Review Letters·J A Ketoja, I I Satija
Dec 16, 1996·Physical Review Letters·M K OberthalerA Zeilinger
Jul 15, 1996·Physical Review Letters·N Hatano, D R Nelson
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·K Schaadt, A Kudrolli

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Citations

May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Indubala I Satija, Arjendu K Pattanayak
Dec 13, 2006·Physical Review Letters·Indubala I SatijaCharles W Clark

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