Statistical fluctuations of the parametric derivative of the transmission and reflection coefficients in absorbing chaotic cavities

TL;DR

This paper investigates the statistical fluctuations of the parametric derivatives of transmission and reflection coefficients in absorbing chaotic cavities, providing analytical variance results applicable to various symmetry and channel configurations.

Contribution

It offers new analytical expressions for the variance of these derivatives in absorbing chaotic cavities, extending previous work to multiple channels and symmetry conditions.

Findings

Variance formulas for transmission and reflection derivatives derived

Results valid for arbitrary number of channels and symmetry conditions

Agreement with existing one-channel non-absorbing case

Abstract

Motivated by recent theoretical and experimental works, we study the statistical fluctuations of the parametric derivative of the transmission T and reflection R coefficients in ballistic chaotic cavities in the presence of absorption. Analytical results for the variance of the parametric derivative of T and R, with and without time-reversal symmetry, are obtained for both asymmetric and left-right symmetric cavities. These results are valid for arbitrary number of channels, in completely agreement with the one channel case in the absence of absorption studied in the literature.