Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
Personal tools
Log in

Disorder in Quantum Systems with Antilinear Symmetries

In this project we investigate the effects of disorder and localization on non-hermitian quantum systems that exhibit a pseudo-hermitian phase, where all of its eigenvalues are real.  Most prominently these are parity-time-symmetric (PT-symmetric) systems and their generalizations. They can be realized in optics by an appropriate arrangement of materials with gain and loss such that the refraction index has the symmetry n(x)=-n*(-x).


In a first step, in collaboration with Boris Shapio, we studied the influence of localized modes in lattices of size N with parity-time (PT) symmetric potentials (refraction indices) [1].  In these systems the spectrum can be real (exact PT-symmetric phase) for some parametric regime of the gain/loss coefficient g<gPT. We have found that as g increases the levels move to the complex plane via an avoided crossing mechanism of localized modes.  The spontaneous PT symmetry breaking occurs at gPT proportional to e-N/l (where l is the localization length), thus resulting in an exponentially narrow exact PT phase.

Contact:  Ragnar Fleischmann 

Members working within this Project:

 Boris Shapiro (DFG FOR760 Fellow) 
 Ragnar Fleischmann 

Former Members:

 Tsampikos Kottos 
 Oliver Bendix 

Selected Publications:

M.C. Zheng, F.M. Ellis, T. Kottos, R. Fleischmann, T. Geisel, and T. Prosen (2011).
Heat transport in active harmonic chains
Phys. Rev. E 84(2):021119. download file

M.C. Zheng, D.N. Christodoulides, R. Fleischmann, and T. Kottos (2010).
PT optical lattices and universality in beam dynamics
Phys. Rev. A 82(1):010103(R). download file

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro (2010).
Optical structures with local PT-symmetry
J. Phys. A 43:265305. download file

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro (2009).
Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
Phys. Rev. Lett. 103(3):030402. download file