Wave systems with direct processes and localized losses or gains: the nonunitary Poisson kernel

Area of Science:

• Quantum mechanics
• Wave scattering theory
• Complex potentials

Background:

• Investigating wave scattering in systems with energy losses or gains is crucial for understanding various physical phenomena.
• Imaginary potentials are used to simulate these non-conservative effects, leading to non-unitary scattering matrices.

Purpose of the Study:

• To analyze the scattering of waves in systems with localized losses or gains.
• To determine the distribution of non-unitary scattering matrices in the Argand plane.
• To analytically derive and numerically verify the nonunitary Poisson kernel for such systems.

Main Methods:

• Simulating wave scattering using a complex delta potential to model absorption or amplification.
• Analyzing the movement of the scattering matrix in the Argand plane.
• Extending analyticity conditions from unitary to non-unitary scattering matrices.
• Comparing numerical simulation results with analytical predictions.

Main Results:

• The scattering matrix in systems with imaginary potentials moves on a specific circle in the Argand plane.
• Numerical simulations show the scattering matrix distribution, measured from the circle's center, matches the nonunitary Poisson kernel.
• Analytical derivations confirm this agreement and extend the findings to measurements from the origin.

Conclusions:

• The nonunitary Poisson kernel accurately describes the distribution of scattering matrices in systems with gains or losses.
• The study provides a robust analytical framework for understanding non-unitary scattering phenomena.
• The findings have implications for fields utilizing wave propagation in dissipative or active media.