Unitarization of the classical statistical s matrix for systems with localization.

Area of Science:

• Quantum chaos
• Mesoscopic physics
• Random matrix theory

Background:

• A classically motivated random S-matrix for a large reverberant cavity was found to be non-unitary.
• A random process with envelope ~ exp(-t/TH) led to a unitary S-matrix with mesoscopic behaviors.
• These behaviors included enhanced backscatter, quantum echo, power law tails, and level repulsion.

Purpose of the Study:

• To extend the procedure of repairing non-unitary S-matrices to systems with internal time scales.
• To investigate coupled rooms and 1D random structures with multiple scattering.
• To analyze the resulting S-matrices for signatures of localization.

Main Methods:

• Applying a minimally invasive procedure to make the S-matrix unitary.
• Modeling random processes with envelopes related to Heisenberg time (TH).
• Analyzing repaired S-matrices for coupled rooms and 1D random structures.

Main Results:

• The repaired S-matrices for coupled rooms and 1D random structures exhibit signatures of localization.
• The study extends previous findings on unitary S-matrices and mesoscopic behaviors.
• Internal time scales related to conduction and diffusion were incorporated.

Conclusions:

• The repaired S-matrices correspond to Wigner K-matrices.
• The presence of internal time scales (conduction, diffusion) alongside Heisenberg time leads to observable quantum phenomena.
• The findings provide insights into quantum transport and localization in complex systems.