Europhys. Lett.
Volume 62, Number 6, June 2003
Page(s) 789 - 794
Section General
Published online 01 June 2003
DOI: 10.1209/epl/i2003-00441-9
Europhys. Lett., 62 (6) , pp. 789-794 (2003)

Critical phenomena associated with self-orthogonality in non-Hermitian quantum mechanics

E. Narevicius1, P. Serra2 and N. Moiseyev1

1  Department of Chemistry and Minerva Center of Nonlinear Physics in Complex Systems Technion, Israel Institute of Technology - Haifa 32000, Israel
2  Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba Ciudad Universitaria - 5000 Córdoba, Argentina

(Received 19 November 2002; accepted in final form 29 April 2003)

The delocalization phenomenon was discovered by Hatano et al. and Miller et al. for a class of non-Hermitian quantum-mechanical problems. We show that the delocalization is only one example of many possible critical phenomena which are associated with the self-orthogonality of an eigenstate of the non-Hermitian Hamiltonian. It is shown that in this class of problems the self-orthogonality occurs at the series of branch points in the complex energy plane that serve as gates for the "particle" to hop from one Bloch energy band to another one.

05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.60.-k - Transport processes.
05.70.Jk - Critical point phenomena.

© EDP Sciences 2003