Finite rank perturbations and solutions to the operator Riccati equation

We consider an off-diagonal self-adjoint finite rank perturbation of a self-adjoint operator in a complex separable Hilbert space $\mathfrak{H}_0 \oplus \mathfrak{H}_1$, where $\mathfrak{H}_1$ is finite dimensional. We describe the singular spectrum of the perturbed operator and establish a connection with solutions to the operator Riccati equation. In particular, we prove existence results for solutions in the case where the whole Hilbert space is finite dimensional.Comment: 13 pages, added Preliminaries, added more detail

Wave packet approach to periodically driven scattering

For autonomous systems it is well known how to extract tunneling probabilities from wavepacket calculations. Here we present a corresponding approach for periodically time-dependent Hamiltonians, valid at all frequencies, field strengths, and transition orders. After mapping the periodically driven system onto a time-independent one with an additional degree of freedom, use is made of the correlation function formulation of scattering [J. Chem. Phys. {\bf 98}, 3884 (1993)]. The formalism is then applied to study the transmission properties of a resonant tunneling double barrier structure under the influence of a sinusoidal laser field, revealing an unexpected antiresonance in the zero photon transition for large field strengths.Comment: 4 pages, 2 figure

Active Brownian particles with velocity-alignment and active fluctuations

We consider a model of active Brownian particles with velocity-alignment in two spatial dimensions with passive and active fluctuations. Hereby, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the heading of an individual active particle. In the simplest case studied here, they are assumed as independent stochastic forces parallel (speed noise) and perpendicular (angular noise) to the velocity of the particle. On the other hand, passive fluctuations are defined by a noise vector independent of the direction of motion of a particle, and may account for example for thermal fluctuations. We derive a macroscopic description of the active Brownian particle gas with velocity-alignment interaction. Hereby, we start from the individual based description in terms of stochastic differential equations (Langevin equations) and derive equations of motion for the coarse grained kinetic variables (density, velocity and temperature) via a moment expansion of the corresponding probability density function. We focus here in particular on the different impact of active and passive fluctuations on the onset of collective motion and show how active fluctuations in the active Brownian dynamics can change the phase-transition behaviour of the system. In particular, we show that active angular fluctuation lead to an earlier breakdown of collective motion and to emergence of a new bistable regime in the mean-field case.Comment: 5 figures, 22 pages, submitted to New Journal of Physic

Dissociation and ionization of small molecules steered by external noise

We show that ionization and dissociation can be influenced separately in a molecule with appropriate external noise. Specifically we investigate the hydrogen molecular ion under a stochastic force quantum mechanically beyond the Born-Oppenheimer approximation. We find that up to 30% of dissociation without ionization can be achieved by suitably tuning the forcing parameters.Comment: 13 pages, 6 figure

Mixed methodology in human brain research: integrating MRI and histology

Postmortem magnetic resonance imaging (MRI) can provide a bridge between histological observations and the in vivo anatomy of the human brain. Approaches aimed at the co-registration of data derived from the two techniques are gaining interest. Optimal integration of the two research fields requires detailed knowledge of the tissue property requirements for individual research techniques, as well as a detailed understanding of the consequences of tissue fixation steps on the imaging quality outcomes for both MRI and histology. Here, we provide an overview of existing studies that bridge between state-of-the-art imaging modalities, and discuss the background knowledge incorporated into the design, execution and interpretation of postmortem studies. A subset of the discussed challenges transfer to animal studies as well. This insight can contribute to furthering our understanding of the normal and diseased human brain, and to facilitate discussions between researchers from the individual disciplines

Coulomb blockade effects in driven electron transport

We study numerically the influence of strong Coulomb repulsion on the current through molecular wires that are driven by external electromagnetic fields. The molecule is described by a tight-binding model whose first and last site is coupled to a respective lead. The leads are eliminated within a perturbation theory yielding a master equation for the wire. The decomposition into a Floquet basis enables an efficient treatment of the driving field. For the electronic excitations in bridged molecular wires, we find that strong Coulomb repulsion significantly sharpens resonance peaks which broaden again with increasing temperature. By contrast, Coulomb blockade has only a small influence on effects like non-adiabatic electron pumping and coherent current suppression.Comment: 9 pages, 7 figures. Added a plot for temperature dependence of resonance peaks. Published versio

Einleitung

Bulst N, Rüthing H. Einleitung. In: Krutisch P, Großmann GU, eds. Der Weserraum zwischen 1500 und 1650: Gesellschaft, Wirtschaft und Kultur in der frühen Neuzeit. Materialien zur Kunst- und Kulturgeschichte in Nord- und Westdeutschland ; 4. Marburg: Jonas-Verl.; 1993: 9-14

Semiclassical description of multiphoton processes

We analyze strong field atomic dynamics semiclassically, based on a full time-dependent description with the Hermann-Kluk propagator. From the properties of the exact classical trajectories, in particular the accumulation of action in time, the prominent features of above threshold ionization (ATI) and higher harmonic generation (HHG) are proven to be interference phenomena. They are reproduced quantitatively in the semiclassical approximation. Moreover, the behavior of the action of the classical trajectories supports the so called strong field approximation which has been devised and postulated for strong field dynamics.Comment: 10 pages, 11 figure