Truncation method for Green's functions in time-dependent fields

We investigate the influence of a time dependent, homogeneous electric field on scattering properties of non-interacting electrons in an arbitrary static potential. We develop a method to calculate the (Keldysh) Green's function in two complementary approaches. Starting from a plane wave basis, a formally exact solution is given in terms of the inverse of a matrix containing infinitely many 'photoblocks' which can be evaluated approximately by truncation. In the exact eigenstate basis of the scattering potential, we obtain a version of the Floquet state theory in the Green's functions language. The formalism is checked for cases such as a simple model of a double barrier in a strong electric field. Furthermore, an exact relation between the inelastic scattering rate due to the microwave and the AC conductivity of the system is derived which in particular holds near or at a metal-insulator transition in disordered systems.Comment: to appear in Phys. Rev. B., 21 pages, 3 figures (ps-files

Universal Conductance and Conductivity at Critical Points in Integer Quantum Hall Systems

The sample averaged longitudinal two-terminal conductance and the respective Kubo-conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, $0.60\pm 0.02 e^2/h$ and $0.58\pm 0.03 e^2/h$, respectively. In the 2nd lowest Landau band, a critical conductance $0.61\pm 0.03 e^2/h$ is obtained which indeed supports the notion of universality. However, these numbers are significantly at variance with the hitherto commonly believed value $1/2 e^2/h$. We argue that this difference is due to the multifractal structure of critical wavefunctions, a property that should generically show up in the conductance at quantum critical points.Comment: 4 pages, 3 figure

Two-Particle Dark State in the Transport through a Triple Quantum Dot

We study transport through a triple quantum dot in a triangular geometry with applied bias such that both singly- and doubly- charged states participate. We describe the formation of electronic dark states -- coherent superpositions that block current flow -- in the system, and focus on the formation of a two-electron dark state. We discuss the conditions under which such a state forms and describe the signatures that it leaves in transport properties such as the differential conductance and shotnoise.Comment: (9 pages, 7 figures), we now consider two different sets of charging energie

Modeling Disordered Quantum Systems with Dynamical Networks

It is the purpose of the present article to show that so-called network models, originally designed to describe static properties of disordered electronic systems, can be easily generalized to quantum-{\em dynamical} models, which then allow for an investigation of dynamical and spectral aspects. This concept is exemplified by the Chalker-Coddington model for the Quantum Hall effect and a three-dimensional generalization of it. We simulate phase coherent diffusion of wave packets and consider spatial and spectral correlations of network eigenstates as well as the distribution of (quasi-)energy levels. Apart from that it is demonstrated how network models can be used to determine two-point conductances. Our numerical calculations for the three-dimensional model at the Metal-Insulator transition point delivers among others an anomalous diffusion exponent of $\eta = 3 - D_2 = 1.7 \pm 0.1$. The methods presented here in detail have been used partially in earlier work.Comment: 16 pages, Rev-TeX. to appear in Int. J. Mod. Phys.

Spin entangled two-particle dark state in quantum transport through coupled quantum dots

We present a transport setup of coupled quantum dots that enables the creation of spatially separated spin-entangled two-electron dark states. We prove the existence of an entangled transport dark state by investigating the system Hamiltonian without coupling to the electronic reservoirs. In the transport regime the entangled dark state which corresponds to a singlet has a strongly enhanced Fano factor compared to the dark state which corresponds to a mixture of the triplet states. Furthermore we calculate the concurrence of the occupying electrons to show the degree of entanglement in the transport regime.Comment: 9 pages and 3 figure

Critical regime of two dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates

The critical two-terminal conductance $g_c$ and the spatial fluctuations of critical eigenstates are investigated for a disordered two dimensional model of non-interacting electrons subject to spin-orbit scattering (Ando model). For square samples, we verify numerically the relation $\sigma_c=1/[2\pi(2-D(1))] e^2/h$ between critical conductivity $\sigma_c=g_c=(1.42\pm 0.005) e^2/h$ and the fractal information dimension of the electron wave function, $D(1)=1.889\pm 0.001$. Through a detailed numerical scaling analysis of the two-terminal conductance we also estimate the critical exponent $\nu=2.80\pm 0.04$ that governs the quantum phase transition.Comment: IOP Latex, 7 figure

Quantum transfer matrix method for one-dimensional disordered electronic systems

We develop a novel quantum transfer matrix method to study thermodynamic properties of one-dimensional (1D) disordered electronic systems. It is shown that the partition function can be expressed as a product of $2\times2$ local transfer matrices. We demonstrate this method by applying it to the 1D disordered Anderson model. Thermodynamic quantities of this model are calculated and discussed.Comment: 7 pages, 10 figure

Better Synchronizability Predicted by Crossed Double Cycle

In this brief report, we propose a network model named crossed double cycles, which are completely symmetrical and can be considered as the extensions of nearest-neighboring lattices. The synchronizability, measured by eigenratio $R$, can be sharply enhanced by adjusting the only parameter, crossed length $m$. The eigenratio $R$ is shown very sensitive to the average distance $L$, and the smaller average distance will lead to better synchronizability. Furthermore, we find that, in a wide interval, the eigenratio $R$ approximately obeys a power-law form as $R\sim L^{1.5}$.Comment: 4 pages, 5 figure

Character of eigenstates of the 3D disordered Anderson Hamiltonian

We study numerically the character of electron eigenstates of the three dimensional disordered Anderson model. Analysis of the statistics of inverse participation ratio as well as numerical evaluation of the electron-hole correlation function confirm that there are no localized states below the mobility edge, as well as no metallic state in the tail of the conductive band. We discuss also finite size effects observed in the analysis of all the discussed quantities.Comment: 7 pages, 9 figures, resubmitted to Physical Review