Table of contents

It is well known that non-Markov processes can be described by means of Markov processes by increasing the dimension of the non-Markov processes. In line with this approach, we derive a description of multivariate stochastic processes with delay in terms of Markov processes. In particular, a multivariate Langevin equation and the corresponding multivariate Fokker–Planck equation is obtained for multivariate systems with delay. In addition, an evolution equation of the Fokker–Planck type for systems with delay is derived that generalizes the evolution equation proposed by Guillouzic et al to the multivariate case. Both Ito and Stratonovich calculus are considered.

The Hamiltonian Stückelberg coupling between p- and (p + 1)-form gauge fields is derived by means of a deformation technique based on local BRST cohomology.

The weak decay η → π⁺π^-ν proceeds mainly via contributions that violate either the isotopic-spin invariance or the OZI rule. An investigation of this decay could therefore, ideally, contribute to an understanding of these mechanisms.

Within the framework of second order time dependent perturbation theory and non relativistic dipole approximation, the exact expressions of the radial transition amplitude from 3d, 3p and 3s excited states, were obtained from the integral representation of the Green Coulomb function. Below threshold and above one photon ionization threshold, it can be expressed as an analytic combination of three Appell hypergeometric functions of first order, one of which is degenerated; while at threshold, it can be obtained in terms of an expansion of Gauss confluent hypergeometric functions. The angular coefficients are numerically evaluated and analysed for some available laser wavelengths.

A small amplitude, modified electron acoustic monotonic double layer in an unmagnetized plasma consisting of relativistic drifting cold electrons and non-relativistic drifting thermal ions is investigated. By using the reductive perturbation method, Korteweg–de Vries (K–dV) like equations are derived. Solving the K–dV like equations of modified electron acoustic waves, we find that simple expressions are obtained for the amplitude and the inverse scale length in a semi-relativistic plasma. We show that all expressions are influenced by relativistic effects. Furthermore, we show that the monotonic double layer solution is a nonlinear extension of the modified electron acoustic solitary hole having negative trapping parameter in a semi-relativistic plasma.

We study the effective electron mass at the Fermi-level on the basis of a newly formulated electron energy spectrum for heavily doped non-parabolic III–V semiconductors forming band-tails, taking n-InSb as an example. The investigation on the mass includes both the presence and absence of band-tailing states, in parabolic and non-parabolic energy band structures, respectively. The effective mass exists in the forbidden region, which is impossible without band-tailing effects. The analyses have been carried out for the Fermi-energy and other entities, like screening length and impurity screening potential, respectively. The values of the effective mass with band-tailing states are found much less as compared with in the absence of band-tails. The well-known results for unperturbed two-band model of Kane have also been obtained from our generalized analysis under certain limiting conditions.

On the basis of analytical calculations for the dynamics of a Bloch electron in two-mode pure ac fields we find a localization condition of the Bloch electron on a localized state that either the ratio edE₁/ω₁ or edE₂/ω₂ of the ac fields is the root of the ordinary zero-order Bessel function J₀ whenever the ratio of frequencies of two ac fields ω₁/ω₂ is not a rational number. The result is also extended to the multi-field case.

Atomic physics has lost in Ugo Fano one of its dominant players during a good part of the 20th century. He has also steadily contributed to this journal during its entire existence as a 'Correspondent'. One of us (HHS) was occupied for a number of years with experiments on the 'Fano Effect' as applied to the intensity ratio anomalies in alkali principal series. This is related to his work on production of polarized electrons by photoionization with polarized light or with polarized atoms. Another (FJdH), together with coworkers at the FOM Institute for Atomic and Molecular Physics, is indebted to Ugo Fano for his stimulation of and his continuous interest in the experiments on total and multiple ionization of noble gas atoms by electron impact. He pointed out to us the relation with photoabsorption by these atoms and the corresponding oscillator strength in the continuum according to the Bethe-Born theory. In addition, the Fano–Lichten theory, describing the promotion of electrons in quasi-molecules formed in keV heavy ion–atom collisions, has been used by us to explain inner-shell ionization and resulting x-rays.

It is important to document the work and lives of eminent physicists who have made seminal contributions to atomic, molecular, and optical physics. This was done recently with the special issue of Comments on Atomic and Molecular Physics on the `Casimir Effect'. We are grateful to Mitio Inokuti and A R P Rau, long-time collaborators of Ugo Fano, for the overview of his life's work, his biography and publications.

With the passing of Ugo Fano on 13 February 2001, Comments on Atomic and Molecular Physics lost a longtime correspondent since its founding in 1969. A broader community dearly misses a great theoretical physicist.

The present tribute is designed in a special way appropriate for this journal, in view of other documents describing Fano's life and work. It is accompanied by a curriculum vitae, which shows the span of a rich professional life. We shall concentrate on his accomplishments in atomic and molecular physics, leaving aside contributions to radiation physics and other areas. We also present a list of his publications, which should be useful as a resource material.

We present a critical discussion about the use of Kinetic Monte Carlo simulations for describing accurately the growth of metal atom nanowires and nanogratings on metallic vicinal surfaces. Aside from the external parameters (temperature, deposition flux, coverage and terrace width) defining the optimum conditions for the formation of low dimension periodic nanostructures, the predictive character of such simulations depends on the diffusion model via the interactions between the adatoms and the surface and between the adatoms themselves. The adequacy and failure of the method are commented using Ag/Pt surface as typical system.

The DNA molecule is composed of two long strands of repeated sugar-phosphate units to which the bases are chemically linked. The two strands are held together by hydrogen bonding between the bases. It is reported that low energy (3–20 eV) electrons interacting with vacuum-dry samples of DNA can break a single strand or both. The incident electron energy dependencies of the yields of single and double strand breaks are compared with those of H^- ions ejected by electron impact on thin films of the elementary constituents of DNA (i.e., H₂O, bases and sugar analogues). The decay of transient anions formed on the DNA's basic components is found to play a crucial role in producing single and double strand breaks. Since a large portion of the energy deposited by ionizing radiation first leads to the production of low energy secondary electrons, these findings provide basic knowledge necessary to understand the effects of high-energy radiation in biological cells and eventually modify these effects at the molecular level.