Caustics occur widely in dynamics and take on shapes classified by catastrophe theory. At finite wavelengths they produce interference patterns containing networks of vortices (phase singularities). ...Here we investigate caustics in quantized fields, focusing on the collective dynamics of quantum spins. We show that, following a quench, caustics are generated in the Fock space amplitudes specifying the many-body configuration and which are accessible in experiments with cold atoms, ions, or photons. The granularity of quantum fields removes all singularities, including phase singularities, converting point vortices into nonlocal vortices that annihilate in pairs as the quantization scale is increased. Furthermore, the continuous scaling laws of wave catastrophes are replaced by discrete versions. Such "quantum catastrophes" are expected to be universal dynamical features of quantized fields.
We examine the tunnelling process of incident Hermite-Gaussian wavepackets which feature several nodes and peaks. An analytic formula for the transmitted wave function is developed which applies to ...arbitrary incident wave functions and potential barriers with known transmission amplitudes. This formula permits the accurate numerical calculation of the transmitted wave packet, even when the transmission probability is extremely small. For square potential barriers, the shape of the transmitted packet, its relationship to the shape of the incident packet, the momentum of the transmitted packet, and the duration of the tunnelling process are investigated. The shape of the reconstructed transmitted wave packet is also studied for the smooth repulsive Pöschl-Teller potential.
Exact analytical results expressed in terms of Bessel functions for the bandgaps, reflectance and transmittance of one-dimensional photonic crystals with a sawtooth refractive index profile on the ...period are derived, to our knowledge for the first time. This extends the set of exactly solvable models with periodic refractive indices. Asymptotic approximations to the above exact results have been also obtained.
This paper concerns analytically solvable cases of Hill's equation containing a continuously differentiable periodic potential. We outline a procedure for constructing the Floquet-Bloch fundamental ...system, and analyze the band structure of the system. The similarities to, and differences from, the cases of a piecewise constant periodic potential and the Mathieu potential, are illuminated.
Band structure of a sawtooth photonic crystal for optical wave propagation along the axis of periodicity is investigated. Floquet–Bloch solutions are found and illustrated for the bandgaps, allowed ...bands, and bandedges of the crystal. Special attention is given to the cases where Floquet–Bloch solutions become periodic functions.
An airfreight container with automated instruments for measurement of atmospheric gases and trace compounds was operated on a monthly basis onboard a Boeing 767-300 ER of LTU International Airways ...during long-distance flights from 1997 to 2002 (CARIBIC, Civil Aircraft for Regular Investigation of the Atmosphere Based on an Instrument Container, http://www.caribic-atmospheric.com). Subsequently a more advanced system has been developed, using a larger capacity container with additional equipment and an improved inlet system. CARIBIC phase #2 was implemented on a new long-range aircraft type Airbus A340-600 of the Lufthansa German Airlines (Star Alliance) in December 2004, creating a powerful flying observatory. The instrument package comprises detectors for the measurement of O3, total and gaseous H2O, NO and NOy, CO, CO2, O2, Hg, and number concentrations of sub-micrometer particles (>4 nm, >12 nm, and >18 nm diameter). Furthermore, an optical particle counter (OPC) and a proton transfer mass spectrometer (PTR-MS) are incorporated. Aerosol samples are collected for analysis of elemental composition and particle morphology after flight. Air samples are taken in glass containers for laboratory analyses of hydrocarbons, halocarbons and greenhouse gases (including isotopic composition of CO2) in several laboratories. Absorption tubes collect oxygenated volatile organic compounds. Three differential optical absorption spectrometers (DOAS) with their telescopes mounted in the inlet system measure atmospheric trace gases such as BrO, HONO, and NO2. A video camera mounted in the inlet provides information about clouds along the flight track. The flying observatory, its equipment and examples of measurement results are reported.
We study coherent electron dynamics in a biased undriven ideal semiconductor superlattice coupled to the continuum, near energy level anticrossings. In particular, we examine the dependence of ...wavepacket dynamical characteristics on electric field detuning, and investigate mixed regimes involving a superposition of energy level anticrossings showing both Rabi oscillations and resonant tunnelling. In earlier work (Abumov and Sprung 2007 Phys. Rev. B 75 165421), Rabi and Zener resonances were shown to have a common origin, and a criterion for the occurrence of either was proposed. The present results allow a better understanding of the nature of an interminiband resonance, which can be useful in the areas of microwave radiation generation and matter manipulation on the particle level, as well as demonstrating an alternative approach to examining electron level structure of a finite superlattice.
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