Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

Critical Excitation Spectrum of Quantum Chain With A Local 3-Spin Coupling

This article reports a measurement of the low-energy excitation spectrum along the critical line for a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields. The measured excitation spectrum agrees with that predicted by the (D$_4$, A$_4$) conformal minimal model under a nontrivial correspondence between translations at the critical line and discrete lattice translations. Under this correspondence, the measurements confirm a prediction that the critical line of this quantum spin chain and the critical point of the 2D 3-state Potts model are in the same universality class.Comment: 7 pages, 2 figure

A computationally efficient method for calculating the maximum conductance of disordered networks: Application to 1-dimensional conductors

Random networks of carbon nanotubes and metallic nanowires have shown to be very useful in the production of transparent, conducting films. The electronic transport on the film depends considerably on the network properties, and on the inter-wire coupling. Here we present a simple, computationally efficient method for the calculation of conductance on random nanostructured networks. The method is implemented on metallic nanowire networks, which are described within a single-orbital tight binding Hamiltonian, and the conductance is calculated with the Kubo formula. We show how the network conductance depends on the average number of connections per wire, and on the number of wires connected to the electrodes. We also show the effect of the inter-/intra-wire hopping ratio on the conductance through the network. Furthermore, we argue that this type of calculation is easily extendable to account for the upper conductivity of realistic films spanned by tunneling networks. When compared to experimental measurements, this quantity provides a clear indication of how much room is available for improving the film conductivity.Comment: 7 pages, 5 figure

Monte Carlo Simulations of Some Dynamical Aspects of Drop Formation

In this work we present some results from computer simulations of dynamical aspects of drop formation in a leaky faucet. Our results, which agree very well with the experiments, suggest that only a few elements, at the microscopic level, would be necessary to describe the most important features of the system. We were able to set all parameters of the model in terms of real ones. This is an additional advantage with respect to previous theoretical works.Comment: 7 pages (Latex), 6 figures (PS) Accepted to publication in Int. J. Mod. Phys. C Source Codes at http://www.if.uff.br/~arlim

Gravastars and Black Holes of Anisotropic Dark Energy

Dynamical models of prototype gravastars made of anisotropic dark energy are constructed, in which an infinitely thin spherical shell of a perfect fluid with the equation of state $p = (1-\gamma)\sigma$ divides the whole spacetime into two regions, the internal region filled with a dark energy fluid, and the external Schwarzschild region. The models represent "bounded excursion" stable gravastars, where the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes. Here we show, for the first time in the literature, a model of gravastar and formation of black hole with both interior and thin shell constituted exclusively of dark energy. Besides, the sign of the parameter of anisotropy ($p_t - p_r$) seems to be relevant to the gravastar formation. The formation is favored when the tangential pressure is greater than the radial pressure, at least in the neighborhood of the isotropic case ($\omega=-1$).Comment: 16 pages, 8 figures. Accepted for publication in Gen. Rel. Gra