3,487 research outputs found
New multidimensional partially integrable generalization of S-integrable N-wave equation
This paper develops a modification of the dressing method based on the
inhomogeneous linear integral equation with integral operator having nonempty
kernel. Method allows one to construct the systems of multidimensional Partial
Differential Equations (PDEs) having the differential polynomial forms in any
dimension n. Associated solution space is not full, although it is parametrized
by a certain number of arbitrary functions of (n-1)-variables. We consider
4-dimensional generalization of the classical (2+1)-dimensional S-integrable
N-wave equation as an example.Comment: 38 page
Ultraviolet-Renormalon Reexamined
We consider large-order perturbative expansions in QED and QCD. The
coefficients of the expansions are known to be dominated by the so called
ultraviolet (UV) renormalons which arise from inserting a chain of
vacuum-polarization graphs into photonic (gluonic) lines. In large orders the
contribution is associated with virtual momenta of order where
is external momentum, is the base of natural logs and is the order
of perturbation theory considered. To evaluate the UV renormalon we develop
formalism of operator product expansion (OPE) which utilizes the observation
that . When applied to the simplest graphs the formalism reproduces
the known results in a compact form. In more generality, the formalism reveals
the fact that the class of the renormalon-type graphs is not well defined. In
particular, graphs with extra vacuum-polarization chains are not suppressed.
The reason is that while inclusion of extra chains lowers the power of their contribution is enhanced by combinatorial factors.Comment: LaTex, 18 pages, 5 figures. Some numerical coefficients are corrected
once mor
Vainshtein mechanism in Gauss-Bonnet gravity and Galileon aether
We derive field equations of Gauss-Bonnet gravity in 4 dimensions after
dimensional reduction of the action and demonstrate that in this scenario
Vainshtein mechanism operates in the flat spherically symmetric background. We
show that inside this Vainshtein sphere the fifth force is negligibly small
compared to the gravitational force. We also investigate stability of the
spherically symmetric solution, clarify the vocabulary used in the literature
about the hyperbolicity of the equation and the ghost-Laplacian stability
conditions. We find superluminal behavior of the perturbation of the field in
the radial direction. However, because of the presence of the non linear terms,
the structure of the space-time is modified and as a result the field does not
propagate in the Minkowski metric but rather in an "aether" composed by the
scalar field . We thereby demonstrate that the superluminal behavior
does not create time paradoxes thank to the absence of Causal Closed Curves. We
also derive the stability conditions for Friedmann Universe in context with
scalar and tensor perturbations.Comment: 9 pages, 5 figures, references added, more details on the
cosmological analysis included, results and conclusions unchanged, final
version to appear in PR
Partially Massless Spin 2 Electrodynamics
We propose that maximal depth, partially massless, higher spin excitations
can mediate charged matter interactions in a de Sitter universe. The proposal
is motivated by similarities between these theories and their traditional
Maxwell counterpart: their propagation is lightlike and corresponds to the same
Laplacian eigenmodes as the de Sitter photon; they are conformal in four
dimensions; their gauge invariance has a single scalar parameter and actions
can be expressed as squares of single derivative curvature tensors. We examine
this proposal in detail for its simplest spin 2 example. We find that it is
possible to construct a natural and consistent interaction scheme to conserved
vector electromagnetic currents primarily coupled to the helicity 1 partially
massless modes. The resulting current-current single ``partial-photon''
exchange amplitude is the (very unCoulombic) sum of contact and shorter-range
terms, so the partial photon cannot replace the traditional one, but rather
modifies short range electromagnetic interactions. We also write the gauge
invariant fourth-derivative effective actions that might appear as effective
corrections to the model, and their contributions to the tree amplitude are
also obtained.Comment: 15 pages, LaTe
Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation
By performing two parallel numerical experiments -- solving the dynamical
Hamiltonian equations and solving the Hasselmann kinetic equation -- we
examined the applicability of the theory of weak turbulence to the description
of the time evolution of an ensemble of free surface waves (a swell) on deep
water. We observed qualitative coincidence of the results.
To achieve quantitative coincidence, we augmented the kinetic equation by an
empirical dissipation term modelling the strongly nonlinear process of
white-capping. Fitting the two experiments, we determined the dissipation
function due to wave breaking and found that it depends very sharply on the
parameter of nonlinearity (the surface steepness). The onset of white-capping
can be compared to a second-order phase transition. This result corroborates
with experimental observations by Banner, Babanin, Young.Comment: 5 pages, 5 figures, Submitted in Phys. Rev. Letter
Generalization of the Fierz-Pauli Action
We consider the Lagrangian of gravity covariantly amended by the mass and
polynomial interaction terms with arbitrary coefficients, and reinvestigate the
consistency of such a theory in the decoupling limit, up to the fifth order in
the nonlinearities. We calculate explicitly the self-interactions of the
helicity-0 mode, as well as the nonlinear mixing between the helicity-0 and -2
modes. We show that ghost-like pathologies in these interactions disappear for
special choices of the polynomial interactions, and argue that this result
remains true to all orders in the decoupling limit. Moreover, we show that the
linear, and some of the nonlinear mixing terms between the helicity-0 and -2
modes can be absorbed by a local change of variables, which then naturally
generates the cubic, quartic, and quintic Galileon interactions, introduced in
a different context. We also point out that the mixing between the helicity-0
and 2 modes can be at most quartic in the decoupling limit. Finally, we discuss
the implications of our findings for the consistency of the effective field
theory away from the decoupling limit, and for the Boulware-Deser problem.Comment: 18 pages, no figure
Two-dimensional ring-like vortex and multisoliton nonlinear structures at the upper-hybrid resonance
Two-dimensional (2D) equations describing the nonlinear interaction between
upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal
nonlinearity in the equations results in the possibility of existence of stable
2D nonlinear structures. A rigorous proof of the absence of collapse in the
model is given. We have found numerically different types of nonlinear
localized structures such as fundamental solitons, radially symmetric vortices,
nonrotating multisolitons (two-hump solitons, dipoles and quadrupoles), and
rotating multisolitons (azimuthons). By direct numerical simulations we show
that 2D fundamental solitons with negative hamiltonian are stable.Comment: 8 pages, 6 figures, submitted to Phys. Plasma
- …