Chaotic quantum transport through spatially symmetric microstructures in the symplectic ensemble

TL;DR

This paper investigates quantum transport in symmetric chaotic microstructures with symplectic symmetry, revealing how this symmetry influences conductance distribution and demonstrates weak anti-localization effects.

Contribution

It provides explicit calculations of conductance distributions for small channel numbers, highlighting the impact of symplectic symmetry on quantum transport phenomena.

Findings

Explicit conductance distributions for N=1 and N=2 channels

Demonstration of weak anti-localization due to symplectic symmetry

Analysis of scattering matrices with spatial symmetry

Abstract

Quantum transport through left-right symmetric chaotic cavities in the presence of the symplectic symmetry, is studied through the statistical distribution of the dimensionless conductance. With this particular point symmetry, their associated scattering matrices are blocky diagonalized by a rotation by an angle of $\pi/4$. Although the formulation is established for an arbitrary number channels N, we present explicit calculations for N=1 and N=2, the last one showing the weak anti-localization phenomenon due to the symplectic symmetry.