ANNOUNCEMENT

A special issue of Acta Mathematica Scientia, to be published in 2011, will be dedicated to the 85th birthday of Peter D. Lax, who is one of the most promi- nent mathematicians of     

Preface

This special issue of Acta Mathematica Scientia is dedicated to the 85th birthday of Peter D. Lax, one of the most prominent mathematicians of the past hundred years. Peter Lax has made important and seminal contributions in many areas of pure and applied mathematics, including the theory of integrable systems and solitons, the     

Evolution of DNA sequences toward recognition of metallic armchair carbon nanotubes

The armchair carbon nanotube is an ideal system to study fundamental physics in one-dimensional metals and potentially a superb material for applications such as electrical power transmission. Synthesis and purification efforts to date have failed to produce a homogeneous population of such a material. Here we report evolutionary strategies to find DNA sequences for the recognition and subsequent purification of (6,6) and (7,7) armchair species from synthetic mixtures. The new sequences were derived by single-point scanning mutation and sequence motif variation of previously identified ones for semiconducting tubes. Optical absorption spectroscopy of the purified armchair tubes revealed well-resolved first- and second-order electronic transitions accompanied by prominent sideband features that have neither been predicted nor observed previously. Resonance Raman spectroscopy showed a single Lorentzian peak for the in-plane carbon-carbon stretching mode (G band) of the armchair tubes, repudiating the common practice of using such a line shape to infer the absence of metallic species. Our work demonstrates the exquisite sensitivity of DNA to nanotube metallicity and makes the long-anticipated pure armchair tubes available as seeds for their mass amplification.     

Stimulated Raman spectra of a strong bichromatic field interacting with a three-level atom

We have studied the stimulated Raman spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes ω _a and ω _b are in resonance with the two atomic transition frequencies. The Green's function formalism has been used in the limit of high photon densities to calculate the excitation spectra near the frequencies ω = ± ω _ab = ± (ω _a - ω _b ). Expressions are derived for the relative intensities, which describe, apart from the usual Raman peak at the frequency ω = ω _ab , four pairs of lorentzian lines peaked at the frequencies ω - ω _ab = ± Ω _a /√2, ± Ω _b /√2, ± Ω and ± 2Ω, respectively, and having spectra widths of the order of 3γ₀/4. The parameter Ω is defined as Ω² = (Ω _a ² + Ω _b ²)/2, where Ω _a and Ω _b are the Rabi frequencies of the two laser fields and γ₀ is the spontaneous emission probability. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. Conditions have been established for which Raman gain processes are anticipated to take place.     

Ordinal decompositions for preordered root systems

In this paper, we explore the effects of certain forbidden substructure conditions on preordered sets. In particular, we characterize in terms of these conditions those preordered sets which can be represented as the supremum of a well-ordered ascending chain of lowersets whose members are constructed by means of alternating applications of disjoint union and ordinal sums with chains. These decompositions are examples of ordinal decompositions in relatively normal lattices as introduced by Snodgrass, Tsinakis, and Hart. We conclude the paper with an application to information systems.     

Nonuniversal transmission phase lapses through a quantum dot: an exact diagonalization of the many-body transport problem

Systematic trends of nonuniversal behavior of electron-transmission phases through a quantum dot, with no phase lapse for the transition N = 1-->N = 2 and a lapse of pi for the N = 2-->N = 3 transition, are predicted, in agreement with experiments, from many-body transport calculations involving exact diagonalization of the dot Hamiltonian. The results favor shape anisotropy of the dot and strong e-e repulsion with consequent electron localization, showing dependence on spin configurations and the participation of excited doorway transmission channels.     

Resonance fluorescence spectrum of a three-level atom

We consider the excitation spectrum arising from the interaction between a three-level atom and a strong electromagnetic field in the frequency region where the two atomic transition frequencies are nearly equal to once and twice the frequency of the pump field respectively. Detailed expressions for the spectral functions are derived describing the two-, one- and zero-photon excitations as well as those arising from the coupling between them, in the limit of high photon densities. The zero-photon excitations describe low frequency modes induced by the pump field under resonance conditions.     

Two-atom two-photon resonance fluorescence

The excitation spectrum arising from the interaction between two identical two-level atoms, one of which is excited in the presence of a strong electromagnetic field (pump field), is investigated when the atomic transition frequency is nearly twice the frequency of the pump field. The excitation spectrum consists of those describing the symmetric and antisymmetric modes, respectively. The spectral functions for the symmetric and antisymmetric modes are derived and discussed in detail. The possibility to measure directly the magnitude of the dipole-dipole interaction energy is discussed.