Time-Ordering and a Generalized Magnus Expansion

Both the classical time-ordering and the Magnus expansion are well known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including, however, directly a non-trivial initial condition. As a by-product we recover a variant of the time-ordering operation, known as ${\mathsf{T}^\ast}$ -ordering. Eventually, placing our results in the general context of Rota–Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations.     

Reduction of the coherence time of an intense laser pulse propagating through a plasma

We present direct measurements of the coherence time of a laser beam after propagation through an underdense plasma. At an intensity of 10(14) W/cm(2), a large decrease of the coherence time is observed, from 300 ps to a few picoseconds. This decrease is larger as the plasma density is increased or as the light is scattered at larger angles. The amount of temporal decorrelation as well as the effect of the plasma density, laser intensity, and scattering angle all coincide with trends observed in recent numerical simulations.     

Modal decomposition method for modeling the interaction of Lamb waves with cracks

The interaction of the low-order antisymmetric (a0) and symmetric (s0) Lamb waves with vertical cracks in aluminum plates is studied. Two types of slots are considered: (a) internal crack symmetrical with respect to the middle plane of the plate and (b) opening crack. The modal decomposition method is used to predict the reflection and transmission coefficients and also the through-thickness displacement fields on both sides of slots of various heights. The model assumes strip plates and cracks, thus considering two-dimensional plane strain conditions. However, mode conversion (a0 into s0 and vice versa) that occurs for single opening cracks is considered. The energy balance is always calculated from the reflection and transmission coefficients, in order to check the validity of the results. These coefficients together with the through-thickness displacement fields are also compared to those predicted using a finite element code widely used in the past for modeling Lamb mode diffraction problems. Experiments are also made for measuring the reflection and transmission coefficients for incident a0 or s0 lamb modes on opening cracks, and compared to the numerical predictions.     

Three-dimensional microfabrication by two-photon-initiated polymerization with a low-cost microlaser

Fabrication of submicrometer structures by two-photon-initiated polymerization is performed with an inexpensive and low-power microlaser. This is made possible by the design of photoinitiators with strong two-photon absorption cross sections. We analyze the influence of both material properties and irradiation conditions on the two-photon polymerization rate and show that resins based on our highly sensitive two-photon photoinitiator can be solidified with microlaser excitation, whereas commercial UV photoresins require ultrashort and intense laser pulses.     

Description of pulse propagation in a dispersive medium by use of a pulse quality factor

We investigated how the duration of short laser pulses evolves in a dispersive material, using rms widths and a propagation law based on a pulse quality factor. Experiments were carried out with femtosecond pulses (10 to 25fs at the temporal waist) propagating in bulk fused silica. Excellent agreement was found between theory and experiment. This approach does not require complete characterization of laser pulses and eliminates the need for any assumption regarding the interpretation of autocorrelation traces. The method is of general validity, and it can be applied to pulses of arbitrary shape.     

Capture by stabilized continuum: Classical and quantum aspects

We review here the results of our investigations concerning chaotic atomic scattering in the presence of a laser field. Particular emphasis is put on the existence of classical stable resonance structures, induced by the intense laser field, which are embedded in the field-free continuum. We show that phase space structures in the vicinity of a resonance island play an important role in the chaotic scattering behavior and form the basis for a mechanism to enhance the lifetimes of the collisional partners. Quantum calculations, based on a wave packet propagation method, show that quantum solutions are strongly influenced by the classical phase space structures. More specifically, a wave packet is found to spread differently in the regular and chaotic regions; in the latter case it spreads exponentially with time until saturation occurs, defining the saturation time. We also investigate the dependence of the spreading rates in both the regular and chaotic regimes. Calculations with an ensemble of classical trajectories are also presented to further illustrate the smoothing effects of varying.     

Spin waves transport across a ferrimagnetically ordered nanojunction of cobalt-gadolinium alloy between cobalt leads

A model calculation is presented for the spin wave scattering and coherent transport at the ferrimagnetically ordered cobalt-gadolinium alloy nanojunction between cobalt leads. The structural model for the amorphous alloy nanojunction [Co_1/2Gd_1/2]₃ is considered as an ordered alloy hcp structure of three (0001) atomic planes between the leads. To analyze the spin dynamics and spin wave scattering at the nanojunction boundary, the phase field matching method (PFMT) is implemented over the ground state of the system, in the Heisenberg Hamiltonian representation. The coherent reflection and transmission probabilities of spin waves from the cobalt leads incident onto the nanojunction boundary are calculated, and numerical results are presented for the coherent SW transport across the nanojunction over the entire range of their frequencies. The results are especially valid in the interval between nanometric SW wavelengths greater than the nanojunction width and macroscopic wavelengths. They demonstrate in particular, the possibility of the resonance assisted maxima for the SW transmission spectra owing to the interactions between the incident spin waves and the localized spin resonances on the nanojunction. This effect is general and may be observed at different characteristic frequencies and corresponding incident angles.     

Stabilisation of fcc cobalt layers by 0.4 nm thick manganese layers in Co/Mn superlattices

Epitaxial Co/Mn multilayers (0.75 to 6 nm Co, 0.4 nm Mn layer thickness) have been grown on mica substrates covered by a (0002) Ru buffer layer. The structural properties of these layers have been studied using X-ray diffraction, nuclear magnetic resonance (NMR), and high resolution transmission electron microscopy (HRTEM). The Co layers, grown as face centred cubic (fcc), were found to be stabilised by the very thin Mn layers. Data obtained using X-ray diffraction and NMR were analysed and found to be in good agreement, while Monte-Carlo simulations were used to interpret the data and calculate the expected diffracted intensity and NMR spectra. The HRTEM data show that the Mn layers give rise to a large strain contrast extending, in the growth direction, over a distance which exceeds the thickness of the Mn layers. The superlattices could be described as having an fcc structure containing randomly located stacking faults with varying densities. The results verify the presence of a dominant, almost perfect phase of fcc stacking, and of a faulted hcp phase, while the number of defects increases with the Co layer thickness. Received 27 October 1999 and Received in final form 29 May 2000     

Probing Proteins in Solution by Xe NMR Spectroscopy

The interaction of xenon with different proteins in aqueous solution is investigated by ¹²⁹Xe NMR spectroscopy. Chemical shifts are measured in horse metmyoglobin, hen egg white lysozyme, and horse cytochrome c solutions as a function of xenon concentration. In these systems, xenon is in fast exchange between all possible environments. The results suggest that nonspecific interactions exist between xenon and the protein exteriors and the data are analyzed in term of parameters which characterize the protein surfaces. The experimental data for horse metmyoglobin are interpreted using a model in which xenon forms a 1:1 complex with the protein and the chemical shift of the complexed xenon is reported (Locci et al., Keystone Symposia “Frontiers of NMR in Molecular Biology VI”, Jan. 9–15, 1999, Breckenridge, CO, Abstract E216, p. 53; Locci et al., XeMAT 2000 “Optical Polarization and Xenon NMR of Materials”, June 28–30, 2000, Sestri Levante, Italy, p. 46).