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PT-symmetric wave Chaos.

Carl T West1, Tsampikos Kottos, Tomaz Prosen

  • 1Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA.

Physical Review Letters
|April 7, 2010
PubMed
Summary

We explore chaotic systems with parity-time (PT) symmetry, finding that chaos aids the transition to a stable phase. This research aids in designing PT-symmetric optical elements.

Area of Science:

  • Nonlinear dynamics
  • Quantum chaos
  • Optics

Background:

  • Parity-time (PT) symmetry in non-Hermitian systems offers unique spectral properties.
  • Dynamical localization can arise in chaotic systems.
  • Gain and loss mechanisms can break Hermiticity while preserving PT symmetry.

Purpose of the Study:

  • To investigate a new class of chaotic systems exhibiting dynamical localization.
  • To analyze the role of gain or loss parameters in PT-symmetric systems.
  • To understand how chaos influences the PT-symmetric phase transition.

Main Methods:

  • Development of a one-parameter scaling theory for the gain/loss parameter (gamma{PT}).
  • Analysis of chaotic systems with engineered gain and loss.

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  • Study of spectral transitions from real to complex values.

    • Main Results:

    • Chaos assists in maintaining the exact PT-symmetric phase.
    • A spontaneous phase transition occurs at a critical gamma{PT} value.
    • The system exhibits dynamical localization due to gain/loss mechanisms.

    Conclusions:

    • Chaos plays a crucial role in stabilizing PT-symmetric phases in non-Hermitian systems.
    • The developed scaling theory provides a framework for understanding these transitions.
    • Findings are applicable to the design of novel PT-symmetric optical devices.