Scattering Theory Approach to Random Schroedinger Operators in One Dimension

Methods from scattering theory are introduced to analyze random Schroedinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the scattering phase by the theorem of Birman and Krein. The spectral shift density is defined as the "thermodynamic limit" of the spectral shift function per unit length of the interaction region. This density is shown to be equal to the difference of the densities of states for the free and the interacting Hamiltonians. Based on this construction, we give a new proof of the Thouless formula. We provide a prescription how to obtain the Lyapunov exponent from the scattering matrix, which suggest a way how to extend this notion to the higher dimensional case. This prescription also allows a characterization of those energies which have vanishing Lyapunov exponent.Comment: 1 figur

Large dimension Configuration Interaction calculations of positron binding to the group II atoms

The Configuration Interaction (CI) method is applied to the calculation of the structures of a number of positron binding systems, including e+Be, e+Mg, e+Ca and e+Sr. These calculations were carried out in orbital spaces containing about 200 electron and 200 positron orbitals up to l = 12. Despite the very large dimensions, the binding energy and annihilation rate converge slowly with l, and the final values do contain an appreciable correction obtained by extrapolating the calculation to the l to infinity limit. The binding energies were 0.00317 hartree for e+Be, 0.0170 hartree for e+Mg, 0.0189 hartree for e+Ca, and 0.0131 hartree for e+Sr.Comment: 13 pages, no figs, revtex format, Submitted to PhysRev

Excited states of positronic atoms

The existence and structure of positronic atoms with a total angular momentum of L=1 is studied with the configuration interaction method. Evidence is presented that there is a P-2(o) state of e(+)Ca and P-2,4(o) states of e(+)Be(P-3(o)) that are electronically stable with binding energies of 45 meV and 2.6 meV, respectively. These predictions rely on the use of an asymptotic series analysis to estimate the angular L ->infinity limit of the energy. Incorporating corrections that compensate for the finite range of the radial basis increased the binding energies of e(+)Ca and e(+)Be to 71 meV and 42 meV, respectively

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

AWAT3.0 - Präzise Bestimmung von Niederschlags- und Verdunstungsereignissen aus Lysimetermessungen mit Hilfe eines verbesserten Datenfilters

Eine genaue Quantifizierung von Evapotranspirations- (ET) und Niederschlagsraten (P) ist für viele Fragen hinsichtlich des Wasser-, Stoff- und Energiehaushalts im System Boden-Pflanze-Atmosphäre von großer Bedeutung. Moderne wägbare Lysimeter mit hoher zeitlicher Auflösung der Gewichtsmessung bieten die präziseste Information für ET und P. Dabei wird ein Ansteigen der Gesamtmasse als P und ein Abfallen als ET interpretiert. Eine Schwierigkeit bei dieser Interpretation ergibt sich daraus, dass die realen Signale durch Messrauschen (z.B. durch Wind) überlagert werden. Wirkliche Signale können in zwei Schritten von Rauschen getrennt werden: (i) Glättung der Daten (z.B. gleitender Mittelwert) mit einem bestimmten Mittelungsfenster und (ii) Einführung eines Schwellenwertes, als Maß für die Messungenauigkeit, der signifikante von nicht signifikanten Masseänderungen trennt. In den letzten Jahren wurden einige Probleme hinsichtlich dieser Vorgehensweise identifiziert und gelöst. Dazu gehören die adaptive Fensterbreite für die Mittelung und der adaptive Schwellenwert für die Trennung von signifikanten von nicht signifikanten Änderungen (Adaptive Window and Adaptive Threshold - AWAT) und eine Interpolation der so gewonnenen Daten, um stufenförmige Änderungen nach der Schwellenwertberechnung zu vermeiden. Ein bisher nicht gelöstes Problem war die systematische Unterschätzung der Flüsse bei jedem Wechsel in der Fließrichtung (von P zu ET oder ET zu P) als Folge der Schwellenwertberechnung. In diesem Beitrag analysieren wir diesen Fehler und schlagen eine heuristische Lösung, die sogenannte „Snap-Routine“, vor. Anhand von synthetischen Daten wird diese Routine kalibriert und getestet. Anschließend wird sie an realen Daten eines „TERENO-Lysimeters“ angewendet. Der systematische Fehler ist unabhängig von der Quantität eines Ereignisses und damit wird der relative Fehler umso größer je kleiner das Ereignis ist. Bei Tau- oder Reifereignissen kann der Fehler dieselbe Größenordnung wie der Fluss haben. Mit der „Snap-Routine“ wird dieser Fehler effektiv behoben, so dass eine Wiedergabe der Flüsse fast ohne systematischen Effekt möglich ist

The Berry-Keating operator on L^2(\rz_>, x) and on compact quantum graphs with general self-adjoint realizations

The Berry-Keating operator H_{\mathrm{BK}}:= -\ui\hbar(x\frac{ \phantom{x}}{ x}+{1/2}) [M. V. Berry and J. P. Keating, SIAM Rev. 41 (1999) 236] governing the Schr\"odinger dynamics is discussed in the Hilbert space L^2(\rz_>, x) and on compact quantum graphs. It is proved that the spectrum of $H_{\mathrm{BK}}$ defined on L^2(\rz_>, x) is purely continuous and thus this quantization of $H_{\mathrm{BK}}$ cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of $H_{\mathrm{BK}}$ acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of $H_{\mathrm{BK}}$. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the "squared" Berry-Keating operator $H_{\mathrm{BK}}^2:= -x^2\frac{ ^2\phantom{x}}{ x^2}-2x\frac{ \phantom{x}}{ x}-{1/4}$ which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for $H_{\mathrm{BK}}^2$ on compact quantum graphs. While the spectra of both $H_{\mathrm{BK}}$ and $H_{\mathrm{BK}}^2$ on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither $H_{\mathrm{BK}}$ nor $H_{\mathrm{BK}}^2$ can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.Comment: 33p

On the absence of bound-state stabilization through short ultra-intense fields

We address the question of whether atomic bound states begin to stabilize in the short ultra-intense field limit. We provide a general theory of ionization probability and investigate its gauge invariance. For a wide range of potentials we find an upper and lower bound by non-perturbative methods, which clearly exclude the possibility that the ultra intense field might have a stabilizing effect on the atom. For short pulses we find almost complete ionization as the field strength increases.Comment: 34 pages Late

A Nanofiber-Based Optical Conveyor Belt for Cold Atoms

We demonstrate optical transport of cold cesium atoms over millimeter-scale distances along an optical nanofiber. The atoms are trapped in a one-dimensional optical lattice formed by a two-color evanescent field surrounding the nanofiber, far red- and blue-detuned with respect to the atomic transition. The blue-detuned field is a propagating nanofiber-guided mode while the red-detuned field is a standing-wave mode which leads to the periodic axial confinement of the atoms. Here, this standing wave is used for transporting the atoms along the nanofiber by mutually detuning the two counter-propagating fields which form the standing wave. The performance and limitations of the nanofiber-based transport are evaluated and possible applications are discussed

An advanced expiratory circuit for the recovery of perfluorocarbon liquid from non-saturated perfluorocarbon vapour during partial liquid ventilation: an experimental model

BACKGROUND: The loss of perfluorocarbon (PFC) vapour in the expired gases during partial liquid ventilation should be minimized both to prevent perfluorocarbon vapour entering the atmosphere and to re-use the recovered PFC liquid. Using a substantially modified design of our previously described condenser, we aimed to determine how much perfluorocarbon liquid could be recovered from gases containing PFC and water vapour, at concentrations found during partial liquid ventilation, and to determine if the amount recovered differed with background flow rate (at flow rates suitable for use in neonates). METHODS: The expiratory line of a standard ventilator circuit set-up was mimicked, with the addition of two condensers. Perfluorocarbon (30 mL of FC-77) and water vapour, at concentrations found during partial liquid ventilation, were passed through the circuit at a number of flow rates and the percentage recovery of the liquids measured. RESULTS: From 14.2 mL (47%) to 27.3 mL (91%) of the infused 30 mL of FC-77 was recovered at the flow rates studied. Significantly higher FC-77 recovery was obtained at lower flow rates (ANOVA with Bonferroni's multiple comparison test, p < 0.0001). As a percentage of the theoretical maximum recovery, 64 to 95% of the FC-77 was recovered. Statistically significantly less FC-77 was recovered at 5 Lmin(-1 )(ANOVA with Bonferroni's multiple comparison test, p < 0.0001). Amounts of perfluorocarbon vapour recovered were 47%, 50%, 81% and 91% at flow rates of 10, 5, 2 and 1 Lmin(-1), respectively. CONCLUSION: Using two condensers in series 47% to 91% of perfluorocarbon liquid can be recovered, from gases containing perfluorocarbon and water vapour, at concentrations found during partial liquid ventilation

Positron-molecule interactions: resonant attachment, annihilation, and bound states

This article presents an overview of current understanding of the interaction of low-energy positrons with molecules with emphasis on resonances, positron attachment and annihilation. Annihilation rates measured as a function of positron energy reveal the presence of vibrational Feshbach resonances (VFR) for many polyatomic molecules. These resonances lead to strong enhancement of the annihilation rates. They also provide evidence that positrons bind to many molecular species. A quantitative theory of VFR-mediated attachment to small molecules is presented. It is tested successfully for selected molecules (e.g., methyl halides and methanol) where all modes couple to the positron continuum. Combination and overtone resonances are observed and their role is elucidated. In larger molecules, annihilation rates from VFR far exceed those explicable on the basis of single-mode resonances. These enhancements increase rapidly with the number of vibrational degrees of freedom. While the details are as yet unclear, intramolecular vibrational energy redistribution to states that do not couple directly to the positron continuum appears to be responsible for these enhanced annihilation rates. Downshifts of the VFR from the vibrational mode energies have provided binding energies for thirty species. Their dependence upon molecular parameters and their relationship to positron-atom and positron-molecule binding energy calculations are discussed. Feshbach resonances and positron binding to molecules are compared with the analogous electron-molecule (negative ion) cases. The relationship of VFR-mediated annihilation to other phenomena such as Doppler-broadening of the gamma-ray annihilation spectra, annihilation of thermalized positrons in gases, and annihilation-induced fragmentation of molecules is discussed.Comment: 50 pages, 40 figure