Variational Monte Carlo and Configurational Interaction Studies of C60C_{60} and its Fragments

The $C_{60}$ molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact calculations. The fragments of $C_{60}$ studied are pyracylene, fluoranthene and corannulene. The energies, bond orders, spin-spin and charge-correlation functions of these systems are obtained for various values of the Hubbard parameter, $U$. The analysis of bond orders and correlation functions of these individual molecules allow us to visualise pyracylene as a naphthalene unit with two ethylenic moieties and fluoranthene as weakly bridged benzene and naphthalene units. Corannulene is the largest fragment of $C_{60}$ that we have studied. The hexagon-hexagon(h-h) bond orders are slightly larger than those of the hexagon-pentagon bonds(h-p), a feature also found in other fragments. We also find bonds between two co-ordinated carbon sites to be stronger than bonds involving three coordinated carbon sites. In $C_{60}$, the h-h bonds are stronger than in corannulene and the h-p bonds weaker than in corannulene for all correlation strengths. Introducing bond alternation in the buckyball enhances this difference.Comment: 42 pages, 5 figures available on request, to appear in J. Phys. Che

On Statistically Convergent and Statistically Cauchy Sequences in Non-Archimedean fields

In this paper, denotes a complete, non-trivially valued non-archimedean field. In the present paper, statistical convergence of sequences and statistically Cauchy sequences are defined and a few theorems on statistically convergent sequences are proved in such field

Offer Price, Target Ownership Structure and IPO Performance

Although the choice of an IPO offer price level would seem to have little economic significance, firms do not decide this arbitrarily. Our findings suggest that firms select their IPO offer prices to target a desired ownership structure, which in turn has implications for underpricing and post-IPO performance. Higher priced IPOs are marketed by more reputed underwriters and attract a relatively larger institutional investment. These IPOs are relatively more underpriced, possibly as compensation for the monitoring and information benefits provided by institutional investors. IPOs whose offer prices are below the median level seem to be targeted towards a retail investor clientele. These IPOs are also relatively more underpriced, possibly as a cost of adverse selection. Our finding that long-run performance increases with offer price confirms that higher priced IPOs are better firms.Initial public offerings; share prices; share allocation

Is Share Price Related to Marketability? Evidence from Mutual Fund Share Splits

We examine the "marketability hypothesis," which states that stock splits enhance the attractiveness of shares to investors by restoring prices to a preferred trading range. We examine splits of mutual fund shares because they provide a clean testing ground for the marketability hypothesis, since the conventional rationales for common stock splits do not apply. We find that splitting funds experience significant increases (relative to non-splitting matched funds) in net assets and shareholders. Stock splits do appear to enhance marketability.

Learning a Neural Semantic Parser from User Feedback

We present an approach to rapidly and easily build natural language interfaces to databases for new domains, whose performance improves over time based on user feedback, and requires minimal intervention. To achieve this, we adapt neural sequence models to map utterances directly to SQL with its full expressivity, bypassing any intermediate meaning representations. These models are immediately deployed online to solicit feedback from real users to flag incorrect queries. Finally, the popularity of SQL facilitates gathering annotations for incorrect predictions using the crowd, which is directly used to improve our models. This complete feedback loop, without intermediate representations or database specific engineering, opens up new ways of building high quality semantic parsers. Experiments suggest that this approach can be deployed quickly for any new target domain, as we show by learning a semantic parser for an online academic database from scratch.Comment: Accepted at ACL 201

Large nonlinear absorption and refraction coefficients of carbon nanotubes estimated from femtosecond Z-scan measurements

Nonlinear transmission of 80 and 140 femtosecond pulsed light with $0.79 \mu m$ wavelength through single walled carbon nanotubes suspended in water containing sodium dodecyl sulphate is studied. Pulse-width independent saturation absorption and negative cubic nonlinearity are observed, respectively, in open and closed aperture Z-scan experiments. The theoretical expressions derived to analyze the z-dependent transmission in the saturable limit require two photon absorption coefficient $\beta_0\sim$ $1.4 cm/MW$ and a nonlinear index $\gamma \sim -5.5 \times10^{-11} cm^2/W$ to fit the data.Comment: 10 pages, 2 figures. Accepted and to appear in Applied Physics Letter

Spin lifetimes of electrons injected into GaAs and GaN

The spin relaxation time of electrons in GaAs and GaN are determined with a model that includes momentum scattering by phonons and ionized impurities, and spin scattering by the Elliot-Yafet, D'yakonov-Perel, and Bir-Aronov-Pikus mechanisms. Accurate bands generated using a long-range tight-binding Hamiltonian obtained from empirical pseudopotentials are used. The inferred temperature-dependence of the spin relaxation lifetime agrees well with measured values in GaAs. We further show that the spin lifetimes decrease rapidly with injected electrons energy and reach a local maximum at the longitudinal optical phonon energy. Our calculation predicts that electron spin lifetime in pure GaN is about 3 orders of magnitude longer than in GaAs at all temperatures, primarily as a result of the lower spin-orbit interaction and higher conduction band density of states.Comment: 8 pages and 3 figure

Estimation of properties of low-lying excited states of Hubbard models : a multi-configurational symmetrized projector quantum Monte Carlo approach

We present in detail the recently developed multi-configurational symmetrized projector quantum Monte Carlo (MSPQMC) method for excited states of the Hubbard model. We describe the implementation of the Monte Carlo method for a multi-configurational trial wavefunction. We give a detailed discussion of issues related to the symmetry of the projection procedure which validates our Monte Carlo procedure for excited states and leads naturally to the idea of symmetrized sampling for correlation functions, developed earlier in the context of ground state simulations. It also leads to three possible averaging schemes. We have analyzed the errors incurred in these various averaging procedures and discuss and detail the preferred averaging procedure for correlations that do not have the full symmetry of the Hamiltonian. We study the energies and correlation functions of the low-lying excited states of the half-filled Hubbard model in 1-D. We have used this technique to study the pair-binding energies of two holes in $4n$ and $4n+2$ systems, which compare well the Bethe ansatz data of Fye, Martins and Scalettar. We have also studied small clusters amenable to exact diagonalization studies in 2-D and have reproduced their energies and correlation functions by the MSPQMC method. We identify two ways in which a multiconfigurational trial wavefunction can lead to a negative sign problem. We observe that this effect is not severe in 1-D and tends to vanish with increasing system size. We also note that this does not enhance the severity of the sign problem in two dimensions.Comment: 29 pages, 2 figures available on request, submitted to Phys. Rev.