Propagation of Gaussian beams in the presence of gain and loss

We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schr\"odinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when the waveguide profile is locally well approximated by quadratic functions. For Hermitian systems, without any loss or gain, these dynamics are given by Hamilton's equations for the center of the beam and its conjugate momentum. Adding gain and/or loss to the waveguide introduces a non-Hermitian component, causing the width of the Gaussian beam to play an important role in its propagation. Here we show how the width affects the motion of the beam and how this may be used to filter Gaussian beams located at the same initial position based on their width

Unexpected local minima in the width complexes for knots

In "Width complexes for knots and 3-manifolds," Jennifer Schultens defines the width complex for a knot in order to understand the different positions a knot can occupy in the 3-sphere and the isotopies between these positions. She poses several questions about these width complexes; in particular, she asks whether the width complex for a knot can have local minima that are not global minima. In this paper, we find an embedding of the unknot that is a local minimum but not a global minimum in its width complex. We use this embedding to exhibit for any knot K infinitely many distinct local minima that are not global minima of the width complex for K.Comment: 9 pages, 4 figure

Unusual localisation effects in quantum percolation

We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focussing on the statistics of the local density of states and the spatial structure of the single particle wavefunctions. Using the Kernel Polynomial Method we refine previous studies of the metal-insulator transition and demonstrate the non-monotonic energy dependence of the quantum percolation threshold. Remarkably, the data indicates a ``fragmentation'' of the spectrum into extended and localised states. In addition, the observation of a chequerboard-like structure of the wavefunctions at the band centre can be interpreted as anomalous localisation.Comment: 5 pages, 7 figure

Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator

The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the anti-Hermitian part. Closed form expressions for the metric and phase-space trajectories are presented which are found to be periodic in time. Since the Hamiltonian is only quadratic the classical dynamics exactly describes the quantum dynamics of Gaussian wave packets. It is shown that the classical metric and trajectories as well as the quantum wave functions can diverge in finite time even though the $PT$-symmetry is unbroken, i.e., the eigenvalues are purely real.Comment: extended version, accepted for publication in J. Phys.

Editorial: Schwerpunktthema "Metadata – Metadaten"

Editorial of the special issue on metadata of the Mitteilungen der Österreichischen Bibliothekarinnen und Bibliothekar

Delocalisation transition in chains with correlated disorder

We show that in the one-dimensional (1D) Anderson model long-range correlations within the sequence of on-site potentials may lead to a region of extended states in the vicinity of the band centre, i.e., to a correlation-induced insulator-metal transition. Thus, although still disordered, the 1D system can behave as a conductor.Comment: 2 pages, 3 figures, submitted to SCES'0

Untergräbt die Stärke der USA die Fundamente der Weltwirtschaft?

Präsident Reagan hat nach landläufiger Meinung erfolgreich die Vitalität der US-Wirtschaftund die Führungsrolle der USA in der Weltwirtschaft wiederhergestellt. Neidisch blickt man von Europa auf die hohen Wachstumsraten der US-Volkswirtschaft, auf die Millionen neuer Arbeitsplätze, auf die massenhaften Investitionen in spitzentechnologischen Bereichen, auf die Flexibilität des Arbeitsmarkts und auf den grenzenlos scheinenden Innovationsdrang USamerikanischer Unternehmen. Eine Revolution scheint sich vor unseren Augen abzuspielen. Der einzige zugegebene Makel: Die USA haben eine beispiellose interne Staatsverschuldung erreicht und sind auf eine massive Kapitaleinfuhr angewiesen (vgl. Schmidt 1985)

Numerische und experimentelle Untersuchungen zum Einfluss von Fluktuationen bei der HCCI-Verbrennung

Zur Modellierung der kontrollierten Selbstzündung in Motoren wird in dieser Arbeit ein Mehrzonenmodell entwickelt. Die chemische Kinetik wird über einen detaillierten Reaktionsmechanismus für einen Benzin Ersatzkraftstoff beschrieben. Das Mehrzonenmodell und der Reaktionsmechanismus werden anhand von experimentellen Ergebnissen validiert. Der experimentelle Teil der Arbeit befasst sich mit der Bestimmung von Fluktuationen in einem optisch zugänglichen Forschungsmotor unter Verwendung von LIF

Optical response of electrons in a random potential

Using our recently developed Chebyshev expansion technique for finite-temperature dynamical correlation functions we numerically study the AC conductivity $\sigma(\omega)$ of the Anderson model on large cubic clusters of up to $100^3$ sites. Extending previous results we focus on the role of the boundary conditions and check the consistency of the DC limit, $\omega\to 0$, by comparing with direct conductance calculations based on a Greens function approach in a Landauer B\"uttiker type setup.Comment: 2 pages, 3 figs, submitted to SCES'0