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

Annihilation contribution and B→a0π,f0KB\to a_0 \pi, f_0 K decays

We analyze the decays $B^0 \to a^\pm_0 \pi^\mp$ and $B^{-,0} \to f_0 K^{-,0}$ and show that within the factorization approximation a phenomenological consistent picture can be obtained. We show that in this approach the $O_6$ operator provides the dominant contributions to the suppressed channel $B^0 \to a^+_0 \pi^-$. When the $a_0$ is considered a two quark state, evaluation of the annihilation form factor using Perturbative $QCD$ implies that this contribution is not negligible, and furthermore it can interfere constructively or destructively with other penguin contributions. As a consequence of this ambiguity, the positive identification of $B^0 \to \pi^+ a_0^-$ can not distinguish between the two or four quark assignment of the $a_0$. According to our calculation, a best candidate to distinguish the nature of $a_0$ scalar is $Br(B^-\to \pi^0a_0^-)$ since the predictions for a four quark model is one order of magnitude smaller than for the two quark assignment. When the scalars are seen as two quarks states, simple theoretical assumptions based on SU(2) isospin symmetry provide relations between different B decays involving one scalar and one pseudoscalar meson.Comment: 12 pages, 3 figure

Covariant tensor formalism for partial wave analyses of ψ\psi decays into γBBˉ\gamma B\bar B, γγV\gamma\gamma V and ψ(2S)→γχc0,1,2\psi(2S)\to\gamma\chi_{c0,1,2} with χc0,1,2→KKˉπ+π−\chi_{c0,1,2}\to K\bar K \pi^+\pi^- and 2π+2π−2\pi^+2\pi^-

With accumulation of high statistics data at BES and CLEO-c, many new interesting channels can get enough statistics for partial wave analysis (PWA). Among them, $\psi \to \gamma p\bar p, \gamma\Lambda\bar \Lambda, \gamma\Sigma \bar\Sigma, \gamma\Xi\bar \Xi$ channels provide a good place for studying baryon-antibaryon interactions; the double radiative decays $\psi\to\gamma\gamma V$ with $V\equiv \rho,\omega,\phi$ have a potential to provide information on the flavor content of any meson resonances (R) with positive charge parity ($C=+$) and mass above 1 GeV through $\psi\to\gamma R \to\gamma\gamma V$; $\psi(2S)\to\gamma\chi_{c0,1,2}$ with $\chi_{c0,1,2}\to K\bar K \pi^+\pi^-$ and $2\pi^+2\pi^-$ decays are good processes to study $\chi_{cJ}$ charmonium decays. Using the covariant tensor formalism, here we provide theoretical PWA formulae for these channels.Comment: 20 page

A review of the decoherent histories approach to the arrival time problem in quantum theory

We review recent progress in understanding the arrival time problem in quantum mechanics, from the point of view of the decoherent histories approach to quantum theory. We begin by discussing the arrival time problem, focussing in particular on the role of the probability current in the expected classical solution. After a brief introduction to decoherent histories we review the use of complex potentials in the construction of appropriate class operators. We then discuss the arrival time problem for a particle coupled to an environment, and review how the arrival time probability can be expressed in terms of a POVM in this case. We turn finally to the question of decoherence of the corresponding histories, and we show that this can be achieved for simple states in the case of a free particle, and for general states for a particle coupled to an environment.Comment: 10 pages. To appear in DICE 2010 conference proceeding

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

On Perturbations of Unitary Minimal Models by Boundary Condition Changing Operators

In this note we consider boundary perturbations in the A-Series unitary minimal models by phi_{r,r+2} fields on superpositions of boundaries. In particular, we consider perturbations by boundary condition changing operators. Within conformal perturbation theory we explicitly map out the space of perturbative renormalisation group flows for the example phi_{1,3} and find that this sheds light on more general phi_{r,r+2} perturbations. Finally, we find a simple diagrammatic representation for the space of flows from a single Cardy boundary condition.Comment: 27 pages, 10 figure

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