The transport of suspended Brownian particles dc-driven along corrugated narrow channels is numerically investigated in the regime of finite damping. We show that inertial corrections cannot be neglected as long as the width of the channel bottleneck
s is smaller than an appropriate particle diffusion length, which depends on the the channel corrugation and the drive intensity. Being such a diffusion length inversely proportional to the damping constant, transport through sufficiently narrow obstructions turns out to be always sensitive to the viscosity of the suspension fluid. The inertia corrections to the transport quantifiers, mobility and diffusivity, markedly differ for smoothly and sharply corrugated channels.
We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely, when the c
onstant drive is parallel to the principal or the diagonal array axes. This corresponds to studying the Brownian transport in periodic channels with reflecting walls of different topologies. The mobility and diffusivity of the transported particles in such channels are determined as functions of the drive and the array geometric parameters. Prominent transport features, like negative differential mobilities, excess diffusion peaks, and unconventional asymptotic behaviors, are explained in terms of two distinct lengths, the size of single obstacles (trapping length) and the lattice constant of the array (local correlation length). Local correlation effects are further analyzed by continuously rotating the drive between the two limiting orientations.
Time-dependent electron transport through a quantum dot and double quantum dot systems in the presence of polychromatic external periodic quantum dot energy-level modulations is studied within the time evolution operator method for a tight-binding Ha
miltonian. Analytical relations for the dc-current flowing through the system and the charge accumulated on a quantum dot are obtained for the zero-temperature limit. It is shown that in the presence of periodic perturbations the sideband peaks of the transmission are related to combination frequencies of the applied modulations. For a double quantum dot system under the influence of polychromatic perturbations the quantum pump effect is studied in the absence of source-drain and static bias voltages. In the presence of spatial symmetry the charge is pumped through the system due to broken generalized parity symmetry.
Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assumi
ng the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW.
Two strongly coupled quantum dots are theoretically and experimentally investigated. In the conductance measurements of a GaAs based low-dimensional system additional features to the Coulomb blockade have been detected at low temperatures. These regi
ons of finite conductivity are compared with theoretical investigations of a strongly coupled quantum dot system and good agreement of the theoretical and the experimental results has been found.
