Pumped current and voltage for an adiabatic quantum pump

We consider adiabatic pumping of electrons through a quantum dot. There are two ways to operate the pump: to create a dc current ${\bar I}$ or to create a dc voltage ${\bar V}$. We demonstrate that, for very slow pumping, ${\bar I}$ and ${\bar V}$ are not simply related via the dc conductance $G$ as $\bar I = \bar V G$. For the case of a chaotic quantum dot, we consider the statistical distribution of ${\bar V} G - {\bar I}$. Results are presented for the limiting cases of a dot with single channel and with multichannel point contacts.Comment: 6 pages, 4 figure

Finite size effects and localization properties of disordered quantum wires with chiral symmetry

Finite size effects in the localization properties of disordered quantum wires are analyzed through conductance calculations. Disorder is induced by introducing vacancies at random positions in the wire and thus preserving the chiral symmetry. For quasi one-dimensional geometries and low concentration of vacancies, an exponential decay of the mean conductance with the wire length is obtained even at the center of the energy band. For wide wires, finite size effects cause the conductance to decay following a non-pure exponential law. We propose an analytical formula for the mean conductance that reproduces accurately the numerical data for both geometries. However, when the concentration of vacancies increases above a critical value, a transition towards the suppression of the conductance occurs. This is a signature of the presence of ultra-localized states trapped in finite regions of the sample.Comment: 5 figures, revtex

Distribution of the reflection eigenvalues of a weakly absorbing chaotic cavity

The scattering-matrix product SS+ of a weakly absorbing medium is related by a unitary transformation to the time-delay matrix without absorption. It follows from this relationship that the eigenvalues of SS+ for a weakly absorbing chaotic cavity are distributed according to a generalized Laguerre ensemble.Comment: 4 pages, 1 figure, to appear in Physica E (special issue on Dynamics of Complex Systems

Weak localization and conductance fluctuations of a chaotic quantum dot with tunable spin-orbit coupling

In a two-dimensional quantum dot in a GaAs heterostructure, the spin-orbit scattering rate is substantially reduced below the rate in a bulk two-dimensional electron gas [B.I. Halperin et al, Phys. Rev. Lett. 86, 2106 (2001)]. Such a reduction can be undone if the spin-orbit coupling parameters acquire a spatial dependence, which can be achieved, e.g., by a metal gate covering only a part of the quantum dot. We calculate the effect of such spatially non-uniform spin-orbit scattering on the weak localization correction and the universal conductance fluctuations of a chaotic quantum dot coupled to electron reservoirs by ballistic point contacts, in the presence of a magnetic field parallel to the plane of the quantum dot.Comment: 4 pages, RevTeX; 2 figures. Substantial revision

Conductance Fluctuations of Open Quantum Dots under Microwave Radiation

We develop a time dependent random matrix theory describing the influence of a time-dependent perturbation on mesoscopic conductance fluctuations in open quantum dots. The effect of external field is taken into account to all orders of perturbation theory, and our results are applicable to both weak and strong fields. We obtain temperature and magnetic field dependences of conductance fluctuations. The amplitude of conductance fluctuations is determined by electron temperature in the leads rather than by the width of electron distribution function in the dot. The asymmetry of conductance with respect to inversion of applied magnetic field is the main feature allowing to distinguish the effect of direct suppression of quantum interference from the simple heating if the frequency of external radiation is larger than the temperature of the leads $\hbar\omega \gg T$.Comment: 7 pages, 5 figure

Delay times and reflection in chaotic cavities with absorption

Absorption yields an additional exponential decay in open quantum systems which can be described by shifting the (scattering) energy E along the imaginary axis, E+i\hbar/2\tau_{a}. Using the random matrix approach, we calculate analytically the distribution of proper delay times (eigenvalues of the time-delay matrix) in chaotic systems with broken time-reversal symmetry that is valid for an arbitrary number of generally nonequivalent channels and an arbitrary absorption rate 1/\tau_{a}. The relation between the average delay time and the ``norm-leakage'' decay function is found. Fluctuations above the average at large values of delay times are strongly suppressed by absorption. The relation of the time-delay matrix to the reflection matrix S^{\dagger}S is established at arbitrary absorption that gives us the distribution of reflection eigenvalues. The particular case of single-channel scattering is explicitly considered in detail.Comment: 5 pages, 3 figures; final version to appear in PRE (relation to reflection extended, new material with Fig.3 added, experiment cond-mat/0305090 discussed

Decay Rate Distributions of Disordered Slabs and Application to Random Lasers

We compute the distribution of the decay rates (also referred to as residues) of the eigenstates of a disordered slab from a numerical model. From the results of the numerical simulations, we are able to find simple analytical formulae that describe those results well. This is possible for samples both in the diffusive and in the localised regime. As example of a possible application, we investigate the lasing threshold of random lasers.Comment: 11 pages, 11 figure

Parametric pumping at finite frequency

We report on a first principles theory for analyzing the parametric electron pump at a finite frequency. The pump is controlled by two pumping parameters with phase difference $\phi$. In the zero frequency limit, our theory predicts the well known result that the pumped current is proportional to $\sin\phi$. For the more general situation of a finite frequency, our theory predicts a non-vanishing pumped current even when the two driving forces are in phase, in agreement with the recent experimental results. We present the physical mechanism behind the nonzero pumped current at $\phi=0$, which we found to be due to photon-assisted processes

Transport Properties and Density of States of Quantum Wires with Off-diagonal Disorder

We review recent work on the random hopping problem in a quasi-one-dimensional geometry of N coupled chains (quantum wire with off-diagonal disorder). Both density of states and conductance show a remarkable dependence on the parity of N. The theory is compared to numerical simulations.Comment: 8 pages, to appear in Physica E (special issue on Dynamics of Complex Systems); 6 figure

Distribution of the reflection eigenvalues of a weakly absorbing chaotic cavity

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