Lanczos cluster expansion for non-extensive systems

A cluster expansion of the Lanczos recursion for non-extensive systems is developed based on the plaquette expansion for extensive systems, in which an auxiliary scaling parameter, Ω, plays the role of volume and introduces extensivity into the problem. Connected Hamiltonian moments of the non-extensive system are computed and introduced into the plaquette expansion in the usual way with Ω. The extensive energy is calculated for increasing orders of the expansion in 1/Ω and the ground state and mass gap of the finite few body problem recovered in the limit Ω → ∞. This new non-perturbative method is applied to the case of N bosons interacting harmonically in one dimension and the ground state energy and mass gap in the vacuum sector are calculated exactly.     

Saturation of resonant frequency conversion processes in cadmium vapour

We have investigated two-photon resonant up conversion of 375 to 159 nm coherent radiation using the four-frequency process ₁₅₉=2₃₇₅+₁₀₄₀ in cadmium vapour, where the ir component (1040 nm) is internally generated by the 375 nm pump tuned to the Cd two-photon transition 5s ^{2 1} S ₀5s6s ¹ S ₀. Scaling laws and tuning behaviour of both the 159 and 1040 nm output power were measured up to 1×10⁸ W cm^–2 pump intensity and 2×10¹⁷ cm^–3 Cd number density. The results are compared to numerical calculations based on semiclassical theory in a stationary perturbation approximation up to third order. Here, in accordance with experimental results, the ir component was assumed to originate from a superposition of stimulated emission and parametric generation. The observed saturation effects turned out to be mainly due to population changes of the atomic levels involved and are qualitatively reproduced by calculations. Discrepancies with respect to absolute output levels are discussed in terms of the approximations in the theoretical formalism.     

Plaquette expansion study of compact U(1) lattice gauge theory in (2 + 1) dimensions

The plaquette expansion is applied to compact U(1) lattice gauge theory in (2 + 1) dimensions to high order: 1/N ⁸ for the ground state energy density and 1/N ⁷ for the anti-symmetric or photon mass gap, where N is defined as the number of plaquettes. Evidence of scaling in the photon mass gap is observed for low order (≤ 1/N ⁴) for inverse coupling values β = 0. 7 to 1. 25 with scaling behaviour given by the weak-coupling formula: M ²/β = exp(-5. 01β + 5. 82) in good agreement with other studies. Higher order results appear to diverge from the scaling slope past the transition point portenting the prospect that the strong coupling trial state in this region gives vise to an asymtotic series in 1/N for the photon mass gap.     

On searching neighbors in computer simulations of macromolecular systems

Various algorithms for evaluating nonbonded interactions in molecular dynamics (MD ) simulations of macromolecular systems are considered, and a combination of two techniques using a space grid for finding neighbor atoms is proposed. The application of grid search techniques to nonrectangular periodic systems is discussed. Finally, the computing time required by different algorithms is compared on a Cray-1 vector processing computer as well as on a CDC Cyber 170/760 sequential computer. Neighbor list techniques turn out to be faster than the grid search techniques for the systems considered here. However, storage requirements may exclude the use of neighbor list techniques for large systems. Finally, MD of complex macromolecular systems turned out to be about 4–14 times faster on a Cray-1 than on a Cyber 170/760.     

Explaining LSND and MiniBooNE using altered neutrino dispersion relations

We investigate the possibility of explaining the MiniBooNE anomaly using CPT-and Lorentz-symmetry-violating neutrino-antineutrino oscillations in a two-generation framework. We work with four non-zero CPT-violating parameters that allow for resonant enhancements in neutrino-antineutrino oscillation phenomena in vacuo which are suitably described in terms of charge conjugation eigenstates of the system. We study the relations among the flavor, charge conjugation and mass eigenbases of neutrino-antineutrino oscillations and examine the interplay between the available CPT-violating parameter space and possible resonance structures.     

Vocal tract resonances and the sound of the Australian didjeridu (yidaki) I. experiment

The didjeridu, or yidaki, is a simple tube about 1.5 m long, played with the lips, as in a tuba, but mostly producing just a tonal, rhythmic drone sound. The acoustic impedance spectra of performers' vocal tracts were measured while they played and compared with the radiated sound spectra. When the tongue is close to the hard palate, the vocal tract impedance has several maxima in the range 1-3 kHz. These maxima, if sufficiently large, produce minima in the spectral envelope of the sound because the corresponding frequency components of acoustic current in the flow entering the instrument are small. In the ranges between the impedance maxima, the lower impedance of the tract allows relatively large acoustic current components that correspond to strong formants in the radiated sound. Broad, weak formants can also be observed when groups of even or odd harmonics coincide with bore resonances. Schlieren photographs of the jet entering the instrument and high speed video images of the player's lips show that the lips are closed for about half of each cycle, thus generating high levels of upper harmonics of the lip frequency. Examples of the spectra of "circular breathing" and combined playing and vocalization are shown.