Generalization of the stabilization method for green functions and quantum resonances

The stabilization method provides an efficient approach to many problems in atomic and molecular dynamics. Real avoided crossings and smoothing techniques provide the relevant information to compute real density of states. The aim of this letter is to present an extension of the stabilization method that allows for a direct determination of full Green functions and resonance energies. The method is based on the use of optical potentials and perturbation theory. Real avoided crossings of the original stabilization method become complex and resonance energies appear to stabilize in the complex-energy plane. A numerical illustration is presented for a simple model of shape resonance. Accurate results are obtained with a small number of real square-integrable functions as in the original stabilization method. The computational efficiency of the approach and its generality are emphasized.     

Higher-Order Simple Lie Algebras

It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order “structure constants”) which characterise the Lie algebra cocycles. This analysis allows us to present a classification of the higher-order simple Lie algebras as well as a constructive procedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra. Received: 3 June 1996 / Accepted: 8 November 1996     

Compact curved-grating stretcher for laser pulse amplification

A compact pulse stretcher using curved diffraction gratings is presented. It introduces positive group-delay dispersion and can operate in conjunction with a standard grating-pair compressor in chirped-pulse amplification systems. It presents several advantages over other systems proposed: It has no degrees of freedom and so is not highly sensitive to alignment errors, it is easy to align, it has a compact and robust design, and it uses standard optics. The frequency-dependent delay, dispersions up to third order, and the design parameters of the stretcher-compressor system that will yield good matching are analyzed. Examples of design specifications for a 40-fs pulse with a central wavelength of lambda=800 nm are given.     

Thermal diffusivity measurements in porous ceramics by photothermal methods

Received: 16 September 1996/Accepted: 6 January 1997     

Analytic solutions of the Schrödinger equation for the modified quartic oscillator

No analytic solutions of the Schrödinger equation are known for the quartic anharmonic oscillator. We show in this paper that there are closely related modified quartic oscillators with the potential depending on |x| for which analytic solutions for some states exist. These results can be extended to the higher order oscillators     

Branching exclusion process on a strip

We consider a model of stochastically interacting particles on an infinite strip of ²; in this model, known as a branching exclusion process, particles jump to each empty neighboring site with rate /4 and also can create a new particle with rate 1/4 at each one of these sites. The initial configuration is assumed to have a rightmost particle and we study the process as seen from the rightmost vertical line occupied. We prove that this process has exactly one invariant measure with the property thatH, the number of empty sites to the left of the rightmost particle, has an exponential moment. This refines a result presented by Bramson {eaet al.}, who proved that ford=1,H is finite with probability 1.     

Anisotropy of the ionic conductivity and dielectric response in orthorhombic and monoclinic inorganic fluorides

The anisotropy of the ionic conductivity and permittivity of (1) BaR₂F₈ (R=rare earth element) single crystals with monoclinic BaTm₂F₈ structure and of (2) (β-YF₃ structured) rare earth trifluorides is studied. Single crystals, eutectic composites and ceramics are investigated in a broad temperature range. In the monoclinic BaR₂F₈ crystals, a pronounced anisotropy of the ionic conductivity and a slight anisotropy of the permittivity are found. The fastest ionic transport with the lowest activation energy (0.563 eV) and the highest value of the permittivity are observed along thea axis. The temperature dependencies of the fluoride ion conductivities of various orthorhombic rare earth trifluorides differ only slightly from one another. For the bulky single crystals, the conductivity at 500 °C and the conduction activation enthalpy are equal to 1.1(4)×10⁻⁵ S/cm and 0.75(3) eV, respectively. The ionic conductivity is almost isotropic, but the anisotropy of the permittivity is significant. For the fluorides of both structural types, plausible conduction mechanisms are proposed, networks of most probable conduction paths are presented and the origin of the observed anisotropy of the ionic conductivity is elucidated. Paper presented at the 4th Euroconference on Solid State Ionics, Renvyle, Galway, Ireland, Sept. 13–19, 1997     

Optimization of some parameters of the gas-flow cems detector measurement

The paper presents, in an abbreviated form, the results of some measurements which were carried out with the aim to obtain an efficient and stable performance of a helium gas-flow CEMS detector.     

Generalized Sasaki Projections and Riesz Ideals in Pseudoeffect Algebras

A noncommutative version of generalized Sasaki projections in pseudoeffect algebras is introduced. It is proved that an ideal in a pseudoeffect algebra is Riesz if and only if it is closed under the right and left Sasaki projections. In lattice ordered pseudoeffect algebras, it is shown that generalized Sasaki projections are one-element sets, and their explicit form is found. It is shown that if a supremum of a normal Riesz ideal in a lattice ordered pseudoeffect algebra exists, it is a central element. These results extend those obtained recently by Avallone and Vitolo for effect algebras.