Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures

A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac’s method to the corresponding action which implies the inclusion of second-class constraints in the formalism which are handled using the procedure of Rothe and Scholtz recently reported. The current method is applied to the non-relativistic two-dimensional isotropic harmonic oscillator employing the various symplectic structures for this dynamical system recently reported.     

Coulomb interaction symmetries and the Mayer series in the two-dimensional dipole gas

We study the Mayer series of the two-dimensional dipole gas in the high-temperature, low-density regime. Without performing any multiscale analysis, we obtain bounds showing that the Mayer coefficients are finite in the thermodynamic limit. These bounds are obtained by exploiting a particular partial symmetry of the interaction (which we nameO-symmetry), already used in some problems related to the two-dimensional Coulomb gas. By direct bounds on some Mayer graphs we also conjecture that any technique based uniquely on theO-symmetry will not be sufficient to prove analyticity of the series.     

Potts Model on Infinite Graphs and the Limit of Chromatic Polynomials

 Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy per site W _r (𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe ³ /q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated in [16 and 19], based on which a sufficient condition for W _r (𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice. Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003 RID="*" ID="*" Partially supported by CNPq (Brazil) RID="**" ID="**" Partially supported by CNR, G.N.F.M. (Italy) Communicated by H. Spohn     

Theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen

The 7σ$7\sigma$ discrepancy between the proton rms charge radius from muonic hydrogen and the CODATA-2010 value from hydrogen spectroscopy and electron-scattering has caused considerable discussions. Here, we review the theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen combining the published contributions and theoretical approaches. The prediction of these quantities is necessary for the determination of both proton charge and Zemach radii from the two 2S–2P transition frequencies measured in muonic hydrogen; see Pohl et al. (2010) [9] and Antognini et al. (2013) [71].     

ATLAS discovery potential for a heavy charged Higgs boson

The sensitivity of the ATLAS detector to the discovery of a heavy charged Higgs boson is presented. Assuming a heavy SUSY spectrum, the most promising channels above the top quark mass are H^± → tb and H^± → τ^±ν_τ which provide coverage in the low and high tanβ regions up to ∼ 600 GeV. The achievable precisions on the charged Higgs mass and tanβ determination are also discussed. The H^± → W^± h⁰ channel, though restricted to a small MSSM parameter space, shows a viable signal in NMSSM where the parameter space is less constrained. The observation of the channel H⁻ → τ⁻_L ν_τ + c.c. may constitute a distinctive evidence for models with singlet neutrinos in large extra dimensions.     

Surface wave effect on light scattering from one-dimensional photonic crystals

Light scattering and reflection measurements using attenuated total reflection technique for s polarization of the incident light on a finite one-dimensional photonic crystal are reported. Angular specular reflection was measured experimentally to determine, the optimum thickness, the angular position of the surface mode, and the number of bi-layers of the system. It was demonstrated that the position of the surface mode inside the last film is close to the asymptotic value when the number of periods is increased. Spectral reflection measurements were made to determine experimentally the band gap width and measure the dispersion relation of the surface mode inside this band. The corresponding field amplitude was calculated (∣E∣²) showing that in resonant conditions it has a maximum near the surface. The angular dependence of the scattered light measured displays a peak caused by singles cattering and located approximately at the excitation angle of the surface electromagnetic mode. When the incident light is in resonance with the surface electromagnetic wave, it is found experimentally that the scattering of light is enhanced overall by approximately one order of magnitude in comparison with the off-resonance case.     

Raman phonon spectra and lattice dynamics of 9,10-dinitroanthracene under pressure

Abstract

Raman phonon spectra of 9, 10-dinitroanthracene have been recorded in the pressure range 0-6GPa. No phase transition is detected up to the maximum pressure studied. Quasi Harmonic Lattice Dynamics calculations, based on an atom-atom potential previously modeled on homologous 9,10-disubstituted anthracenes, have been performed. The optimized potential was used to calculate the equilibrium geometry and the lattice phonon frequencies as a function of pressure. The calculated structure at ambient conditions closely resembles the experimental one. The calculated phonon frequencies show a good agreement with the experimental values at all pressures measured.