Amplitude equations for a linear wave equation in a weakly curved pipe

We study boundary effects in a linear wave equation with Dirichlet type conditions in a weakly curved pipe. The coordinates in our pipe are prescribed by a given small curvature with finite range, while the pipe's cross section being circular. Based on the straight pipe case a perturbative analysis by which the boundary value conditions are exactly satisfied is employed. As such an analysis we decompose the wave equation into a set of ordinary differential equations perturbatively. We show the conditions when secular terms due to the curbed boundary appear in the naive peturbative analysis. In eliminating such a secularity with a singular perturbation method, we derive amplitude equations and show that the eigenfrequencies in time are shifted due to the curved boundary.Comment: To appear in J Phys A: Math. Theo

Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models

Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on four arbitrary parameters is found. For the $A_{n-1}$ models all diagonal solutions are found. The associated integrable magnetic Hamiltonians are explicitly derived.Comment: 9 pages,latex, LPTHE-PAR 92-4

Phonon-assisted tunneling in interacting suspended single wall carbon nanotubes

Transport in suspended metallic single wall carbon nanotubes in the presence of strong electron-electron interaction is investigated. We consider a tube of finite length and discuss the effects of the coupling of the electrons to the deformation potential associated to the acoustic stretching and breathing modes. Treating the interacting electrons within the framework of the Luttinger liquid model, the low-energy spectrum of the coupled electron-phonon system is evaluated. The discreteness of the spectrum is reflected in the differential conductance which, as a function of the applied bias voltage, exhibits three distinct families of peaks. The height of the phonon-assisted peaks is very sensitive to the parameters. The phonon peaks are best observed when the system is close to the Wentzel-Bardeen singularity.Comment: 14 pages, 3 figure

The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition

We analytically derive the spectrum of gravitational waves due to magneto-hydrodynamical turbulence generated by bubble collisions in a first-order phase transition. In contrast to previous studies, we take into account the fact that turbulence and magnetic fields act as sources of gravitational waves for many Hubble times after the phase transition is completed. This modifies the gravitational wave spectrum at large scales. We also model the initial stirring phase preceding the Kolmogorov cascade, while earlier works assume that the Kolmogorov spectrum sets in instantaneously. The continuity in time of the source is relevant for a correct determination of the peak position of the gravitational wave spectrum. We discuss how the results depend on assumptions about the unequal-time correlation of the source and motivate a realistic choice for it. Our treatment gives a similar peak frequency as previous analyses but the amplitude of the signal is reduced due to the use of a more realistic power spectrum for the magneto-hydrodynamical turbulence. For a strongly first-order electroweak phase transition, the signal is observable with the space interferometer LISA.Comment: 46 pages, 17 figures. Replaced with revised version accepted for publication in JCA

Tracing CP-violation in Lepton Flavor Violating Muon Decays

Although the Lepton Flavor Violating (LFV) decay $\mu^+\to e^+ \gamma$ is forbidden in the Standard Model (SM), it can take place within various theories beyond the SM. If the branching ratio of this decay saturates its present bound [{\it i.e.,} Br$(\mu^+ \to e^+\gamma)\sim 10^{-11}$], the forthcoming experiments can measure the branching ratio with high precision and consequently yield information on the sources of LFV. In this letter, we show that for polarized $\mu^+$, by studying the angular distribution of the transversely polarized positron and linearly polarized photon we can derive information on the CP-violating sources beyond those in the SM. We also study the angular distribution of the final particles in the decay $\mu^+\to e^+_1 e^- e^+_2$ where $e^+_1$ is defined to be the more energetic positron. We show that transversely polarized $e_1^+$ can provide information on a certain combination of the CP-violating phases of the underlying theory which would be lost by averaging over the spin of $e^+_1$.Comment: 6 pages, 2 figure

Renormalization of Hamiltonian Field Theory; a non-perturbative and non-unitarity approach

Renormalization of Hamiltonian field theory is usually a rather painful algebraic or numerical exercise. By combining a method based on the coupled cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian approach to renormalization, we show that a powerful and elegant method exist to solve such problems. The method is in principle non-perturbative, and is not necessarily unitary.Comment: 16 pages, version shortened and improved, references added. To appear in JHE

Finite-temperature Screening and the Specific Heat of Doped Graphene Sheets

At low energies, electrons in doped graphene sheets are described by a massless Dirac fermion Hamiltonian. In this work we present a semi-analytical expression for the dynamical density-density linear-response function of noninteracting massless Dirac fermions (the so-called "Lindhard" function) at finite temperature. This result is crucial to describe finite-temperature screening of interacting massless Dirac fermions within the Random Phase Approximation. In particular, we use it to make quantitative predictions for the specific heat and the compressibility of doped graphene sheets. We find that, at low temperatures, the specific heat has the usual normal-Fermi-liquid linear-in-temperature behavior, with a slope that is solely controlled by the renormalized quasiparticle velocity.Comment: 9 pages, 5 figures, Submitted to J. Phys.