SgpDec : Cascade (de)compositions of finite transformation semigroups and permutation groups

We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade products.Final Accepted Versio

New insights into the structure of nanoporous carbons from NMR, Raman, and pair distribution function analysis

The structural characterization of nanoporous carbons is a challenging task as they generally lack long-range order and can exhibit diverse local structures. Such characterization represents an important step toward understanding and improving the properties and functionality of porous carbons, yet few experimental techniques have been developed for this purpose. Here we demonstrate the application of nuclear magnetic resonance (NMR) spectroscopy and pair distribution function (PDF) analysis as new tools to probe the local structures of porous carbons, alongside more conventional Raman spectroscopy. Together, the PDFs and the Raman spectra allow the local chemical bonding to be probed, with the bonding becoming more ordered for carbide-derived carbons (CDCs) synthesized at higher temperatures. The ring currents induced in the NMR experiment (and thus the observed NMR chemical shifts for adsorbed species) are strongly dependent on the size of the aromatic carbon domains. We exploit this property and use computer simulations to show that the carbon domain size increases with the temperature used in the carbon synthesis. The techniques developed here are applicable to a wide range of porous carbons and offer new insights into the structures of CDCs (conventional and vacuum-annealed) and coconut shell-derived activated carbons

Ultrafast changes in lattice symmetry probed by coherent phonons

The electronic and structural properties of a material are strongly determined by its symmetry. Changing the symmetry via a photoinduced phase transition offers new ways to manipulate material properties on ultrafast timescales. However, in order to identify when and how fast these phase transitions occur, methods that can probe the symmetry change in the time domain are required. We show that a time-dependent change in the coherent phonon spectrum can probe a change in symmetry of the lattice potential, thus providing an all-optical probe of structural transitions. We examine the photoinduced structural phase transition in VO2 and show that, above the phase transition threshold, photoexcitation completely changes the lattice potential on an ultrafast timescale. The loss of the equilibrium-phase phonon modes occurs promptly, indicating a non-thermal pathway for the photoinduced phase transition, where a strong perturbation to the lattice potential changes its symmetry before ionic rearrangement has occurred.Comment: 14 pages 4 figure

Ultrafast electronic and lattice dynamics in laser-excited crystalline bismuth

Femtosecond spectroscopy is applied to study transient electronic and lattice processes in bismuth. Components with relaxation times of 1 ps, 7 ps and ~ 1 ns are detected in the photoinduced reflectivity response of the crystal. To facilitate the assignment of the observed relaxation to the decay of particular excited electronic states we use pump pulses with central wavelengths ranging from 400 nm to 2.3 mum. Additionally, we examine the variation of parameters of coherent A1g phonons upon the change of excitation and probing conditions. Data analysis reveals a significant wavevector dependence of electron-hole and electron- phonon coupling strength along \Gamma--T direction of the Brillouin zone.Comment: 19 pages, 9 figure

Calculations of the A_1 phonon frequency in photoexcited Tellurium

Calculations of the A_1 phonon frequency in photoexcited tellurium are presented. The phonon frequency as a function of photoexcited carrier density and phonon amplitude is determined. Recent pump probe experiments are interpreted in the light of these calculatons. It is proposed that, in conjunction with measurements of the phonon period in ultra-fast pump-probe reflectivity experiments, the calculated frequency shifts can be used to infer the evolution of the density of photoexcited carriers on a sub-picosecond time-scale.Comment: 15 pages Latex, 3 postscript figure

Physical properties of misfit-layered (Bi,Pb)-Sr-Co-O system: Effect of hole doping into triangular lattice formed by low-spin Co ions

Pb-doping effect on physical properties of misfit-layered (Bi,Pb)-Sr-Co-O system, in which Co ions form a two-dimensional triangular lattice, was investigated in detail by electronic transport, magnetization and specific-heat measurements. Pb doping enhances the metallic behavior, suggesting that carriers are doped. Pb doping also enhances the magnetic correlation in this system and increases the magnetic transition temperature. We found the existence of the short-range magnetic correlation far above the transition temperature, which seems to induce the spin-glass state coexisting with the ferromagnetic long-range order at low temperatures. Specific-heat measurement suggests that the effective mass of the carrier in (Bi,Pb)-Sr-Co-O is not enhanced so much as reported in NaCo${}_2$O${}_4$. Based on these experimental results, we propose a two-bands model which consists of narrow $a_{1g}$ and rather broad $e'{}_g$ bands. The observed magnetic property and magnetotransport phenomena are explained well by this model

Dirac-Foldy term and the electromagnetic polarizability of the neutron

We reconsider the Dirac-Foldy contribution $\mu^2/m$ to the neutron electric polarizability. Using a Dirac equation approach to neutron-nucleus scattering, we review the definitions of Compton continuum ($\bar{\alpha}$), classical static ($\alpha^n_E$), and Schr\"{o}dinger ($\alpha_{Sch}$) polarizabilities and discuss in some detail their relationship. The latter $\alpha_{Sch}$ is the value of the neutron electric polarizability as obtained from an analysis using the Schr\"{o}dinger equation. We find in particular $\alpha_{Sch} = \bar{\alpha} - \mu^2/m$ , where $\mu$ is the magnitude of the magnetic moment of a neutron of mass $m$. However, we argue that the static polarizability $\alpha^n_E$ is correctly defined in the rest frame of the particle, leading to the conclusion that twice the Dirac-Foldy contribution should be added to $\alpha_{Sch}$ to obtain the static polarizability $\alpha^n_E$.Comment: 11 pages, RevTeX, to appear in Physical Review

Coherent Phonons in Carbon Nanotubes and Graphene

We review recent studies of coherent phonons (CPs) corresponding to the radial breathing mode (RBM) and G-mode in single-wall carbon nanotubes (SWCNTs) and graphene. Because of the bandgap-diameter relationship, RBM-CPs cause bandgap oscillations in SWCNTs, modulating interband transitions at terahertz frequencies. Interband resonances enhance CP signals, allowing for chirality determination. Using pulse shaping, one can selectively excite speci!c-chirality SWCNTs within an ensemble. G-mode CPs exhibit temperature-dependent dephasing via interaction with RBM phonons. Our microscopic theory derives a driven oscillator equation with a density-dependent driving term, which correctly predicts CP trends within and between (2n+m) families. We also find that the diameter can initially increase or decrease. Finally, we theoretically study the radial breathing like mode in graphene nanoribbons. For excitation near the absorption edge, the driving term is much larger for zigzag nanoribbons. We also explain how the armchair nanoribbon width changes in response to laser excitation.Comment: 48 pages, 41 figure