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.