Exponentially Fragile PT Symmetry in Lattices with Localized Eigenmodes

被引：264

作者：

Bendix, Oliver ^{[1
]}

Fleischmann, Ragnar ^{[1
]}

Kottos, Tsampikos ^{[2
]}

Shapiro, Boris ^{[3
]}

机构：

[1] MPI Dynam & Self Org, Gottingen, Germany

[2] Wesleyan Univ, Middletown, CT 06459 USA

[3] Technion Israel Inst Technol, IL-32000 Haifa, Israel

来源：

PHYSICAL REVIEW LETTERS | 2009年 / 103卷 / 03期

关键词：

STATES;

D O I：

10.1103/PhysRevLett.103.030402

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting delta similar to exp(-N/xi) where xi is their localization length. The level "evolution" with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous PT symmetry breaking occurs at gamma PT similar to min{delta}, thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gamma PT similar to 1/N(2) and the distribution P(gamma PT) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.

引用

页数：4

共 16 条

[1]

ALTSHULER BL, 1989, ZH EKSP TEOR FIZ+, V95, P348

[2] ABSENCE OF DIFFUSION IN CERTAIN RANDOM LATTICES [J].