On the electron energy spectrum in heavily doped non-parabolic semiconductors

An attempt is made to present a simple theoretical analysis of the energy-wave vector dispersion relation of the conduction electrons in heavily doped non-parabolic semiconductors forming band tails. We observe that the complex energy spectrum in doped small-gap materials whose unperturbed conduction band is described by the three band model of Kane is due to the interaction of the impurity atoms in the tail with the spin-orbit splitting constant of the valence band (Δ), For band-gap (E_g)<Δ the imaginary part predominates which tails in to the conduction band. For the opposite inequality the real part comes in to play which tails in to the split-off band. In the absence of the band tailing effect, the imaginary part of the complex energy spectrum vanishes and the same is also true for doped two-band Kane-type and parabolic energy bands respectively. The present formulation helps us in investigating the Boltzmann transport equation dependent transport properties of degenerate semiconductors and are expected to agree better with experiments. The well-known results of unperturbed three and two band models of Kane together with wide-gap parabolic energy bands have been obtained as special cases of our generalized analysis under certain limiting conditions.     

Breathers in ferrimagnetic systems

Breathers in discrete nonlinear ferrimagnetic spin lattices are investigated for both easy-axis and easy-plane configurations. The region in frequency space of the formation of breathers is determined and the anticontinuum limit discussed. The monochromatic and the coloured breathers are found out numerically for different parameters and different conditions of excitations.     

Canonical measures on the moduli spaces of compact Riemann surfaces

We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus. This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to the Hodge metric on the Hodge bundle.     

Diff (S 1) and the Teichmüller spaces

Precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations, , carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex analytic Kähler manifolds. These areN=Diff(S ¹)/Rot(S ¹) andM=Diff(S ¹)/Möb(S ¹). Note thatN is a holomorphic disc fiber space overM. Now,M can be naturally considered as embedded in the classical universal Teichmüller spaceT(1), simply by noting that a diffeomorphism ofS ¹ is a quasisymmetric homeomorphism.T(1) is itself a homomorphically homogeneous complex Banach manifold. We prove in the first part of the paper that the inclusion ofM inT(1) iscomplex analytic.In the latter portion of this paper it is shown that theunique homogeneous Kähler metric carried byM = Diff (S ¹/SL(2, ) induces preciselythe Weil-Petersson metric on the Teichmüller space. This is via our identification ofM as a holomorphic submanifold of universal Teichmüller space. Now recall that every Teichmüller spaceT(G) of finite or infinite dimension is contained canonically and holomorphically withinT(1). Our computations allow us also to prove that everyT(G), G any infinite Fuchsian group, projects out ofM transversely. This last assertion is related to the fractal nature ofG-invariant quasicircles, and to Mostow rigidity on the line.Our results thus connect the loop space approach to bosonic string theory with the sum-over-moduli (Polyakov path integral) approach.     

Synthesis and characterization of cobalt(II), nickel(II), copper(II), palladium(II) and dioxouranium(VI) complexes of the antipyrine Schiff base of 3-formylsalicylic acid

A new Schiff base has been synthesized from 4-aminoantipyrine and 3-formylsalicylic acid. The ligand has a dianionic tetradentate compartmental OONO donor system. The cobalt(II), nickel(II), copper(II) and dioxouranium(VI) complexes exist in phenolato-bridged dinuclear species, while palladium(II) gives a mononuclear complex with free –COOH groups. The complexes have been characterized by elemental analyses, i.r., u.v.-vis, thermal and magnetic measurements.     

Accumulation of radiocesium by <Emphasis Type="Italic">Pleurotus citrinopileatus</Emphasis> species of edible mushroom

Pleurotus citrinopileatus, a species of edible mushrooms, is widely accepted food component, especially in Indian subcontinent. The accumulating susceptibility of this edible mushroom species towards long-lived radioisotopes of cesium was studied in controlled laboratory condition using the ¹³⁴Cs (T _1/2 = 2.06 y) radioisotope. It was observed that the experimental mushroom species accumulated ¹³⁴Cs and maximum accumulation took place in the cap portion. The pileus (cap)/stipes (stem) ratio of each ¹³⁴Cs accumulated mushroom sample was determined and found 2.22±0.74. The protein and fat fractions of the experimental mushroom species were extracted separately after accumulation of radiocesium and it was found that most of the radiocesium accumulation occurred in the protein fraction of the mushroom. The mushroom Pleurotus citrinopileatus which is white in color, turned completely black after radiocesium accumulation. The black mushroom so obtained was produced upto fourth generation by tissue culture method without using any radiocesium further. All the successors were found to be black indicating a permanent mutation of the mushroom species.     

Synthesis,Crystal Structure and Thermal Behavior of Gadolinium Dicyanamide Dihydrate Gd[N(CN)2]3 · 2 H2O

Gadolinium dicyanamide dihydrate Gd[N(CN)₂]₃ · 2 H₂O was prepared by ion exchange in aqueous solution followed by evaporation of the solvent at room temperature. Gd[N(CN)₂]₃ · 2 H₂O was characterized by single‐crystal structure analysis, FTIR spectroscopy and DSC analysis. In the crystal there are three crystallographically independent [N(CN)₂]^? ions and Gd³⁺ which are coordinated by six N atoms from six different [N(CN)₂]^? ions and two O atoms from two water molecules forming an irregular quadratic antiprism. Four H bonds have been identified in the structure of Gd[N(CN)₂]₃ · 2 H₂O, two of them running to terminal N atoms and two to the bridging N atoms of dicyanamide ions (Gd[N(CN)₂]₃ · 2 H₂O: P2₁/n (no. 14), a = 7.4845(15) Å, b = 11.529(2) Å, c = 13.941(3) Å, β = 93.98(3)°, Z = 4, 1948 reflections, 175 parameters, R1 = 0.0493). The DSC analysis indicates that Gd[N(CN)₂]₃ · 2 H₂O looses the crystal water at temperatures around 130 – 140 °C forming anhydrous Gd[N(CN)₂]₃, the structure of which has been refined by the Rietveld method based on X‐ray powder diffraction data. Gd[N(CN)₂]₃ was found to be isotypic with Ln[N(CN)₂]₃ (Ln = La, Ce, Pr, Nd, Sm and Eu) which previously have been described in the literature.     

Platinum chromophore-based systems for photoinduced charge separation: a molecular design approach for artificial photosynthesis

Photoinduced charge separation is a fundamental step in photochemical energy conversion. In the design of molecularly based systems for light-to-chemical energy conversion, this step is studied through the construction of two- and three-component systems (dyads and triads) having suitable electron donor and acceptor moieties placed at specific positions on a charge-transfer chromophore. The most extensively studied chromophores in this regard are ruthenium(II) tris(diimine) systems with a common 3MLCT excited state, as well as related ruthenium(II) bis(terpyridyl) systems. This Forum contribution focuses on dyads and triads of an alternative chromophore, namely, platinum(II) di- and triimine systems having acetylide ligands. These d8 chromophores all possess a 3MLCT excited state in which the lowest unoccupied molecular orbital is a pi orbital on the heterocyclic aromatic ligand. The excited-state energies of these Pt(II) chromophores are generally higher than those found for the ruthenium(II) tris(diimine) systems, and the directionality of the charge transfer is more certain. The first platinum diimine bis(arylacetylide) triad, constructed by attaching phenothiazene donors to the arylacetylide ligands and a nitrophenyl acceptor to 5-ethynylphenanthroline of the chromophore, exhibited a charge-separated state of 75-ns duration. The first Pt(tpy)(arylacetylide)+-based triad contains a trimethoxybenzamide donor and a pyridinium acceptor and has been structurally characterized. The triad has an edge-to-edge separation between donor and acceptor fragments of 27.95 Angstroms. However, while quenching of the emission is complete for this system, transient absorption (TA) studies reveal that charge transfer does not move onto the pyridinium acceptor. A new set of triads described in detail here and having the formula [Pt(NO2phtpy)(p-C triple-bond C-C6H4CH2(PTZ-R)](PF6), where NO2phtpy = 4'-{4-[2-(4-nitrophenyl)vinyl]phenyl}-2,2';6',2'-terpyridine and PTZ = phenothiazine with R = H, OMe, possess an unsaturated linkage between the chromophore and a nitrophenyl acceptor. While the parent chromophore [Pt(ttpy)(C triple-bond CC6H5)]PF6 is brightly luminescent in a fluid solution at 298 K, the triads exhibit complete quenching of the emission, as do the related donor-chromophore (D-C) dyads. Electrochemically, the triads and D-C dyads exhibit a quasi-reversible oxidation wave corresponding to the PTZ ligand, while the R = H triad and related C-A dyad display a facile quasi-reversible reduction assignable to the acceptor. TA spectroscopy shows that one of the triads possesses a long-lived charge-separated state of approximately 230 ns.     

Schiffer variation of complex structure and coordinates for Teichmüller spaces

Schiffer variation of complex structure on a Riemann surfaceX ₀ is achieved by punching out a parametric disc \(\bar D\) fromX ₀ and replacing it by another Jordan domain whose boundary curve is a holomorphic image of \(\partial \bar D\) . This change of structure depends on a complex parameter ε which determines the holomorphic mapping function around \(\partial \bar D\) . It is very natural to look for conditions under which these ε-parameters provide local coordinates for Teichmüller spaceT(X ₀), (or reduced Teichmüller spaceT ^#(X₀)). For compactX ₀ this problem was first solved by Patt [8] using a complicated analysis of periods and Ahlfors' [2] τ-coordinates. Using Gardiner's [6], [7] technique, (independently discovered by the present author), of interpreting Schiffer variation as a quasi conformal deformation of structure, we greatly simplify and generalize Patt's result. Theorems 1 and 2 below take care of all the finitedimensional Teichmüller spaces. In Theorem 3 we are able to analyse the situation for infinite dimensionalT(X ₀) also. Variational formulae for the dependence of classical moduli parameters on the ε's follow painlessly.