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

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.

Multifractal magnetoconductance fluctuations in mesoscopic systems.

We perform a multifractal detrended fluctuation analysis of the magnetoconductance data of two standard types of mesoscopic systems: a disordered nanowire and a ballistic chaotic billiard, with two different lattice structures. We observe in all cases that multifractality is generally present and that it becomes stronger in the quantum regime of conduction, i.e., when the number of open scattering channels is small. We argue that this behavior originates from correlations induced by the magnetic field, which can be characterized through the distribution of conductance increments in the corresponding "stochastic time series," with the magnetic field playing the role of a fictitious time. More specifically, we show that the distributions of conductance increments are well fitted by q Gaussians and that the value of the parameter q is a useful quantitative measure of multifractality in magnetoconductance fluctuations.