Interactions of Hermitian and non-Hermitian Hamiltonians

The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number of soluble models. It is found that in all cases the energy remains real for small values of the coupling constant, but becomes complex if the coupling becomes stronger than some critical value. For a quadratic non-Hermitian PT-symmetric Hamiltonian coupled to an arbitrary real Hermitian PT-symmetric Hamiltonian, the reality of the ground-state energy for small enough coupling constant is established up to second order in perturbation theory.Comment: 9 pages, 0 figure

A High Phase Advance Damped and Detuned Structure for the Main Linacs of Clic

The main accelerating structures for the CLIC are designed to operate at an average accelerating gradient of 100 MV/m. The accelerating frequency has been optimised to 11.994 GHz with a phase advance of 2{\pi}/3 of the main accelerating mode. The moderately damped and detuned structure (DDS) design is being studied as an alternative to the strongly damped WDS design. Both these designs are based on the nominal accelerating phase advance. Here we explore high phase advance (HPA) structures in which the group velocity of the rf fields is reduced compared to that of standard (2{\pi}/3) structures. The electrical breakdown strongly depends on the fundamental mode group velocity. Hence it is expected that electrical breakdown is less likely to occur in the HPA structures. We report on a study of both the fundamental and dipole modes in a CLIC_DDS_HPA structure, designed to operate at 5{\pi}/6 phase advance per cell. Higher order dipole modes in both the standard and HPA structures are also studied

Propagation of the phase of solar modulation

The phase of the 11 year galactic cosmic ray variation, due to a varying rate of emission of long lived propagating regions of enhanced scattering, travels faster than the scattering regions themselves. The radial speed of the 11 year phase in the quasi-steady, force field approximation is exactly twice the speed of the individual, episodic decreases. A time dependent, numerical solution for 1 GeV protons at 1 and 30 Au gives a phase speed which is 1.85 times the propagation speed of the individual decreases

The Propagation and Survival of Interstellar Grains

In this paper we discuss the propagation of dust through the interstellar medium (ISM), and describe the destructive effects of stellar winds, jets, and supernova shock waves on interstellar dust. We review the probability that grains formed in stellar outflows or supernovae survive processing in and propagation through the ISM, and incorporate themselves relatively unprocessed into meteoritic bodies in the solar system. We show that very large (radii >= 5 micron) and very small grains (radii <= 100 Angstrom) with sizes similar to the pre-solar SiC and diamond grains extracted from meteorites, can survive the passage through 100\kms shock waves relatively unscathed. High velocity (>= 250 km/s) shocks destroy dust efficiently. However, a small (~10%) fraction of the stardust never encountered such fast shocks before incorporation into the solar system. All grains should therefore retain traces of their passage through interstellar shocks during their propagation through the ISM. The grain surfaces should show evidence of processing due to sputtering and pitting due to small grain cratering collisions on the micron-sized grains. This conclusion seems to be in conflict with the evidence from the large grains recovered from meteorites which seem to show little interstellar processing.Comment: 19 pages, 5 figures (.eps), LaTeX, to appear in "Astrophysical Implications of the Laboratory Study of Presolar Materials" AIP Conference Proceedings, 1997 T.J. Bernatowicz and E. Zinner (eds.

Enhanced coupling design of a detuned damped structure for clic

The key feature of the improved coupling design in the Damped Detuned Structure (DDS) is focused on the four manifolds. Rectangular geometry slots and rectangular manifolds are used. This results in a significantly stronger coupling to the manifolds compared to the previous design. We describe the new design together with its wakefield damping properties.Comment: 3 pages, 8 figures, submitted to IPAC1

WKB Analysis of PT-Symmetric Sturm-Liouville problems

Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered the Schroedinger eigenvalue problem on an infinite domain. This paper examines the consequences of imposing the boundary conditions on a finite domain. As is the case with regular Hermitian Sturm-Liouville problems, the eigenvalues of the PT-symmetric Sturm-Liouville problem grow like $n^2$ for large $n$. However, the novelty is that a PT eigenvalue problem on a finite domain typically exhibits a sequence of critical points at which pairs of eigenvalues cease to be real and become complex conjugates of one another. For the potentials considered here this sequence of critical points is associated with a turning point on the imaginary axis in the complex plane. WKB analysis is used to calculate the asymptotic behaviors of the real eigenvalues and the locations of the critical points. The method turns out to be surprisingly accurate even at low energies.Comment: 11 pages, 8 figure

Variations of the Mid-IR Aromatic Features Inside and Among Galaxies

We present the results of a systematic study of mid-IR spectra of Galactic regions, Magellanic HII regions, and galaxies of various types (dwarf, spiral, starburst), observed by the satellites ISO and Spitzer. We study the relative variations of the 6.2, 7.7, 8.6 and 11.3 micron features inside spatially resolved objects (such as M82, M51, 30 Doradus, M17 and the Orion Bar), as well as among 90 integrated spectra of 50 objects. Our main results are that the 6.2, 7.7 and 8.6 micron bands are essentially tied together, while the ratios between these bands and the 11.3 micron band varies by one order of magnitude. This implies that the properties of the PAHs are remarkably universal throughout our sample, and that the relative variations of the band ratios are mainly controled by the fraction of ionized PAHs. In particular, we show that we can rule out both the modification of the PAH size distribution, and the mid-infrared extinction, as an explanation of these variations. Using a few well-studied Galactic regions (including the spectral image of the Orion Bar), we give an empirical relation between the I(6.2)/I(11.3) ratio and the ionization/recombination ratio G0/ne.Tgas^0.5, therefore providing a useful quantitative diagnostic tool of the physical conditions in the regions where the PAH emission originates. Finally, we discuss the physical interpretation of the I(6.2)/I(11.3) ratio, on galactic size scales.Comment: Accepted by the ApJ, 67 pages, 70 figure

Use of Equivalent Hermitian Hamiltonian for PTPT-Symmetric Sinusoidal Optical Lattices

We show how the band structure and beam dynamics of non-Hermitian $PT$-symmetric sinusoidal optical lattices can be approached from the point of view of the equivalent Hermitian problem, obtained by an analytic continuation in the transverse spatial variable $x$. In this latter problem the eigenvalue equation reduces to the Mathieu equation, whose eigenfunctions and properties have been well studied. That being the case, the beam propagation, which parallels the time-development of the wave-function in quantum mechanics, can be calculated using the equivalent of the method of stationary states. We also discuss a model potential that interpolates between a sinusoidal and periodic square well potential, showing that some of the striking properties of the sinusoidal potential, in particular birefringence, become much less prominent as one goes away from the sinusoidal case.Comment: 11 pages, 8 figure

Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules

Superselection rules (SSRs) limit the mechanical and quantum processing resources represented by quantum states. However SSRs can be violated using reference systems to break the underlying symmetry. We show that there is a duality between the ability of a system to do mechanical work and to act as a reference system. Further, for a bipartite system in a globally symmetric pure state, we find a triality between the system's ability to do local mechanical work, its ability to do ``logical work'' due to its accessible entanglement, and its ability to act as a shared reference system.Comment: 5 pages, no figures. Extended resubmitted version. Slightly modified title. Transferred to PR