Superuniversal Statistics of Complex Time Delays in Non-Hermitian Scattering Systems

Area of Science:

• Complex Systems and Wave Scattering
• Non-Hermitian Physics
• Quantum Chaos

Background:

• Wigner-Smith time delay quantifies excitation residence time in flux conserving systems.
• Complex generalization of time delay for non-Hermitian systems and its statistical properties remain under-developed, especially in the short-wavelength limit of chaotic scattering.
• Previous studies on time-delay statistics primarily focused on unitary systems.

Purpose of the Study:

• To investigate the statistical properties of complex Wigner-Smith time delay and related time-delay differences in non-Hermitian chaotic scattering systems.
• To identify universal behaviors in the statistical distributions of time delays, particularly in the presence of scattering singularities.
• To compare the statistical properties with those of unitary scattering systems.

Main Methods:

• Experimental measurement of multiport scattering (S) matrices from 1D graphs, 2D billiards, and 3D cavities.
• Calculation of complex Wigner-Smith time delay (τ_{WS}), reflection time delays (τ_{xx}), and transmission time delays (τ_{xy}).
• Introduction and calculation of complex reflection time-delay differences (τ_{δR}) and transmission time-delay differences (τ_{δT}) for nonreciprocal systems.

Main Results:

• Large time delays are linked to scattering singularities like coherent perfect absorption and unidirectional invisibility.
• The large-delay tails of the real and imaginary parts of all calculated time-delay quantities exhibit superuniversality, independent of system parameters (D, M, β, η).
• This superuniversality contrasts with unitary systems, where time-delay statistics depend on M and β.

Conclusions:

• The statistical distributions of time delays in non-Hermitian chaotic systems are governed by topological properties of scattering singularities.
• The discovered superuniversality provides a universal framework for understanding the abundance of singularities in generic scattering systems.
• Findings are applicable to various non-Hermitian wave-chaotic systems in the short-wavelength limit, including optical and acoustic resonators.