Universal statistics of the local Green's function in quantum chaotic systems with absorption

TL;DR

This paper derives a universal relation linking the statistics of the local Green's function in chaotic systems with absorption to their correlation functions without absorption, providing explicit formulas applicable across symmetry classes.

Contribution

It introduces a fluctuation dissipation relation for the local Green's function in chaotic systems with absorption, enabling explicit analytical expressions for all symmetry classes.

Findings

Derived explicit joint distribution of real and imaginary parts of Green's function.

Established a fluctuation dissipation relation connecting absorption and correlation functions.

Applicable to experimental impedance and reflection measurements in microwave cavities.

Abstract

We establish a general relation between the statistics of the local Green's function for systems with chaotic wave scattering and a uniform energy loss (absorption) and its two-point correlation function for the same system without absorption. Within the random matrix approach this kind of a fluctuation dissipation relation allows us to derive the explicit analytical expression for the joint distribution function of the real and imaginary parts of the local Green function for all symmetry classes as well as at an arbitrary degree of the time-reversal symmetry breaking in the system. The outstanding problem of the orthogonal symmetry is further reduced to simple quadratures. The results can be applied, in particular, to the experimentally accessible impedance and reflection in a microwave cavity attached to a single-mode antenna.