815 research outputs found
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 . For the six vertex model the general solution
depending on four arbitrary parameters is found. For the 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
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
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 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], 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 , 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 where is defined to be the more energetic positron. We show
that transversely polarized 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 .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.
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