Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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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