Localization in Hermitian and non-Hermitian random chains

The Anderson localization, though originally proposed for the electronic conduction in disordered metals, is now recognized as a ubiquitous phenomenon that occurs when a wave tries to propagate in a random medium. The incident wave, when it interferes with waves randomly scattered by the medium, may not be allowed to propagate throughout the system, in other words, may be localized.

We here show yet another incident of the Anderson localization in a non-Hermitian random chain [1,2]. Before going into the main topic, however, we first review a study in '90s when we introduce a non-Hermitian gauge field to Hermitian random chains [3]. We were able to obtain the localization length, a piece of information on the eigenvectors, only from the complex spectrum of eigenvalues. This fact carries onto the non-Hermitian random chain, whose complex spectrum changes in a interesting way when a non-Hermitian gauge field is introduced.

This work is under collaboration with Ariel Amir, David Nelson and Joshua Feinberg.

References

[1] A. Amir, N. Hatano and D.R. Nelson, PRE 93, 042310 (2016) [2] N. Hatano and J. Feinberg, arXiv:1603.06187 (2016) [3] N. Hatano and D.R. Nelson, PRL 77, 570 (1996); PRB 56, 8651 (1997)