Adelic Amplitudes and Intricacies of Infinite Products

For every prime number $p$ it is possible to define a $p$-adic version of the Veneziano amplitude and its higher-point generalizations. Multiplying together the real amplitude with all its $p$-adic counterparts yields the adelic amplitude. At four points it has been argued that the adelic amplitude, after regulating the product that defines it, equals one. For the adelic 5-point amplitude, there exist kinematic regimes where no regularization is needed. This paper demonstrates that in special cases within this regime, the adelic product can be explicitly evaluated in terms of ratios of the Riemann zeta function, and observes that the 5-point adelic amplitude is not given by a single analytic function. Motivated by this fact to study new regularization procedures for the 4-point amplitude, an alternative formalism is presented, resulting in non-constant amplitudes that are piecewise analytic in the three scattering channels, including one non-constant adelic amplitude previously suggested in the literature. Decomposing the residues of these amplitudes into weighted sums of Gegenbauer polynomials, numerical evidence indicates that in special ranges of spacetime dimensions all the coefficients are positive, as required by unitarity.Comment: 41 pages, 4 figure

Superconductivity in Boron under pressure - why are the measured Tc_c's so low?

Using the full potential linear muffin-tin orbitals (FP-LMTO) method we examine the pressure-dependence of superconductivity in the two metallic phases of Boron: bct and fcc. Linear response calculations are carried out to examine the phonon frequencies and electron-phonon coupling for various lattice parameters, and superconducting transition temperatures are obtained from the Eliashberg equation. In both bct and fcc phases the superconducting transition temperature T$_c$ is found to decrease with increasing pressure, due to stiffening of phonons with an accompanying decrease in electron-phonon coupling. This is in contrast to a recent report, where T$_c$ is found to increase with pressure. Even more drastic is the difference between the measured T$_c$, in the range 4-11 K, and the calculated values for both bct and fcc phases, in the range 60-100 K. The calculation reveals that the transition from the fcc to bct phase, as a result of increasing volume or decreasing pressure, is caused by the softening of the X-point transverse phonons. This phonon softening also causes large electron-phonon coupling for high volumes in the fcc phase, resulting in coupling constants in excess of 2.5 and T$_c$ nearing 100 K. We discuss possible causes as to why the experiment might have revealed T$_c$'s much lower than what is suggested by the present study. The main assertion of this paper is that the possibility of high T$_c$, in excess of 50 K, in high pressure pure metallic phases of boron cannot be ruled out, thus substantiating the need for further experimental investigations of the superconducting properties of high pressure pure phases of boron.Comment: 16 pages, 8 figures, 1 Tabl

pp-adic Holography from the Hyperbolic Fracton Model

We reveal a low-temperature duality between the hyperbolic lattice model featuring fractons and infinite decoupled copies of Zabrodin's $p$-adic model of AdS/CFT. The core of the duality is the subsystem symmetries of the hyperbolic fracton model, which always act on both the boundary and the bulk. These subsystem symmetries are associated with fractal trees embedded in the hyperbolic lattice, which have the same geometry as Zabrodin's model. The fracton model, rewritten as electrostatics theory on these trees, matches the equation of motion of Zabrodin's model. The duality extends from the action to lattice defects as $p$-adic black holes.Comment: 6 pages, 5 figures, and appendi

Role of dynamical screening in excitation kinetics of biased quantum wells: Nonlinear absorption and ultrabroadband terahertz emission

Turchinovich D, Monozon BS, Jepsen PU. Role of dynamical screening in excitation kinetics of biased quantum wells: Nonlinear absorption and ultrabroadband terahertz emission. Journal of Applied Physics. 2006;99(1).In this work we describe the ultrafast excitation kinetics of a biased quantum well, arising from the optically induced dynamical screening of a bias electric field. The initial bias electric field inside the quantum well is screened by the optically excited polarized electron-hole pairs. This leads to a dynamical modification of the properties of the system within an excitation pulse duration. We calculate the excitation kinetics of a biased quantum well and the dependency of resulting electronic and optical properties on the excitation pulse fluence, quantum well width, and initial bias field strength. Our calculations, in particular, predict the strongly nonlinear dependency of the effective optical absorption coefficient on the excitation pulse fluence, and ultrabroadband terahertz emission. Our theoretical model is free of fitting parameters. Calculations performed for internally biased InGaN∕GaN quantum wells are in good agreement with our experimental observations [Turchinovich et al., Phys. Rev. B 68, 241307(R) (2003)], as well as in perfect compliance with qualitative considerations

Covalent bonding and the nature of band gaps in some half-Heusler compounds

Half-Heusler compounds \textit{XYZ}, also called semi-Heusler compounds, crystallize in the MgAgAs structure, in the space group $F\bar43m$. We report a systematic examination of band gaps and the nature (covalent or ionic) of bonding in semiconducting 8- and 18- electron half-Heusler compounds through first-principles density functional calculations. We find the most appropriate description of these compounds from the viewpoint of electronic structures is one of a \textit{YZ} zinc blende lattice stuffed by the \textit{X} ion. Simple valence rules are obeyed for bonding in the 8-electron compound. For example, LiMgN can be written Li$^+$ + (MgN)$^-$, and (MgN)$^-$, which is isoelectronic with (SiSi), forms a zinc blende lattice. The 18-electron compounds can similarly be considered as obeying valence rules. A semiconductor such as TiCoSb can be written Ti$^{4+}$ + (CoSb)$^{4-}$; the latter unit is isoelectronic and isostructural with zinc-blende GaSb. For both the 8- and 18-electron compounds, when \textit{X} is fixed as some electropositive cation, the computed band gap varies approximately as the difference in Pauling electronegativities of \textit{Y} and \textit{Z}. What is particularly exciting is that this simple idea of a covalently bonded \textit{YZ} lattice can also be extended to the very important \textit{magnetic} half-Heusler phases; we describe these as valence compounds \textit{ie.} possessing a band gap at the Fermi energy albeit only in one spin direction. The \textit{local} moment in these magnetic compounds resides on the \textit{X} site.Comment: 18 pages and 14 figures (many in color

Dynamic range in terahertz time-domain transmission and reflection spectorscopy

Peter Uhd Jepsen and Bernd M. Fische