Random-hopping approach to fluctuation phenomena in quantum dots with chiral symmetry.

Abstract

We propose a numerical approach to study mesoscopic fluctuations in quantum dots with chiral symmetry. Our method involves applying the random-hopping model to a tight-binding Hamiltonian, allowing us to calculate the conductance and shot-noise power distributions for systems belonging to the three chiral symmetry classes of random matrix theory. Furthermore, we demonstrate that the spectral fluctuations of quantum dots belonging to the Wigner-Dyson symmetry classes of random matrix theory can be obtained by applying the random-hopping model to a scattering region that was originally integrable, thus bypassing the need to use the boundaries of chaotic billiards.