$\cal{PT}$ -symmetry Wave Chaos

ORAL

Abstract

We study a new class of chaotic systems with dynamical localization, where gain/loss processes break the hermiticity, while allowing for parity-time ${\cal PT}$ symmetry. For a value $\gamma_{\cal PT}$ of the gain/loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for $\gamma_{\cal PT}$, and show that chaos assists the exact ${\cal PT}$-phase. Our results will have applications to the design of optical elements with ${\cal PT}$-symmetry.

*This work was supported by the DFG FOR760 and a grant from the US-Israel Binational Science Foundation (BSF), Jerusalem, Israel.

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Authors

  • Carl T. West

    • Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA \& MPI for Dynamics and Self-Organization, 37073 G\"ottingen, Germany

  • Tsampikos Kottos

    • Wesleyan University and MPI for Dynamics and Self-Organization
    • Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA \& MPI for Dynamics and Self-Organization, 37073 G\"ottingen, Germany
    • Physics Dept., Wesleyan University, Middletown, CT
    • Wesleyan University

  • Tomaz Prosen

    • Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia