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

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

Dynamics of interacting transport qubits

We investigate the electronic transport through two parallel double quantum dots coupled both capacitively and via a perpendicularly aligned charge qubit. The presence of the qubit leads to a modification of the coherent tunnel amplitudes of each double quantum dot. We study the influence of the qubit on the electronic steady state currents through the system, the entanglement between the transport double quantum dots, and the back action on the charge qubit. We use a Born-Markov-Secular quantum master equation for the system. The obtained currents show signatures of the qubit. The stationary qubit state may be tuned and even rendered pure by applying suitable voltages. In the Coulomb diamonds it is also possible to stabilize pure entangled states of the transport double quantum dots

A Sparse Stress Model

Force-directed layout methods constitute the most common approach to draw general graphs. Among them, stress minimization produces layouts of comparatively high quality but also imposes comparatively high computational demands. We propose a speed-up method based on the aggregation of terms in the objective function. It is akin to aggregate repulsion from far-away nodes during spring embedding but transfers the idea from the layout space into a preprocessing phase. An initial experimental study informs a method to select representatives, and subsequent more extensive experiments indicate that our method yields better approximations of minimum-stress layouts in less time than related methods.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Equation of motion method for Full Counting Statistics: Steady state superradiance

For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of cumulant generating function and system operators at lowest order, allows us to recover master equation results of the Full Counting Statistics for certain parameter regimes at very low cost of computation. The thermodynamic limit, that is not accessible with the master equation approach, can be derived analytically for different approximations.Comment: 7 pages, 3 figures, revised version, accepted by PR

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

On large-scale diagonalization techniques for the Anderson model of localization

We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shift-and-invert techniques in the implicitly restarted Lanczos method and in the Jacobi–Davidson method. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete LDLT factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization by several orders of magnitude

Centrality scaling in large networks

Betweenness centrality lies at the core of both transport and structural vulnerability properties of complex networks, however, it is computationally costly, and its measurement for networks with millions of nodes is near impossible. By introducing a multiscale decomposition of shortest paths, we show that the contributions to betweenness coming from geodesics not longer than L obey a characteristic scaling vs L, which can be used to predict the distribution of the full centralities. The method is also illustrated on a real-world social network of 5.5*10^6 nodes and 2.7*10^7 links