230 research outputs found
Discrete singular integrals in a half-space
We consider Calderon -- Zygmund singular integral in the discrete half-space
, where is entire lattice () in ,
and prove that the discrete singular integral operator is invertible in
) iff such is its continual analogue. The key point for
this consideration takes solvability theory of so-called periodic Riemann
boundary problem, which is constructed by authors.Comment: 9 pages, 1 figur
The Use of Dispersion Relations in the and Coupled-Channel System
Systematic and careful studies are made on the properties of the IJ=00
and coupled-channel system, using newly derived dispersion
relations between the phase shifts and poles and cuts. The effects of nearby
branch point singularities to the determination of the resonance are
estimated and and discussed.Comment: 22 pages with 5 eps figures. A numerical bug in previous version is
fixed, discussions slightly expanded. No major conclusion is change
Long-Time Asymptotics for the Toda Lattice in the Soliton Region
We apply the method of nonlinear steepest descent to compute the long-time
asymptotics of the Toda lattice for decaying initial data in the soliton
region. In addition, we point out how to reduce the problem in the remaining
region to the known case without solitons.Comment: 18 page
On slip pulses at a sheared frictional viscoelastic/ non deformable interface
We study the possibility for a semi-infinite block of linear viscoelastic
material, in homogeneous frictional contact with a non-deformable one, to slide
under shear via a periodic set of ``self-healing pulses'', i.e. a set of
drifting slip regions separated by stick ones. We show that, contrary to
existing experimental indications, such a mode of frictional sliding is
impossible for an interface obeying a simple local Coulomb law of solid
friction. We then discuss possible physical improvements of the friction model
which might open the possibility of such dynamics, among which slip weakening
of the friction coefficient, and stress the interest of developing systematic
experimental investigations of this question.Comment: 23 pages, 3 figures. submitted to PR
Order p^6 chiral couplings from the scalar K Pi form factor
Employing results from a recent determination of the scalar KPi form factor
F_0^KPi within a coupled channel dispersion relation analysis \cite{JOP01}, in
this work we calculate the slope and curvature of F_0^KPi(t) at zero momentum
transfer. Knowledge of the slope and curvature of the scalar KPi form factor,
together with a recently calculated expression for F_0^KPi(t) in chiral
perturbation theory at order p^6, enable to estimate the O(p^6) chiral
constants C_12^r=(0.3 +- 5.4)10^-7 and (C_12^r+C_34^r)=(3.2 +- 1.5)10^-6. Our
findings also allow to estimate the contribution coming from the C_i to the
vector form factor F_+^KPi(0) which is crucial for a precise determination of
|V_us| from K_l3 decays. Our result F_+^KPi(0)|_C_i^r=-0.018 +- 0.009, though
inflicted with large uncertainties, is in perfect agreement with a previous
estimate by Leutwyler and Roos already made twenty years ago.Comment: 19 pages, discussion of scale dependence of the chiral couplings
added; version to appear in JHE
On the exceptional case of the characteristic singular equation with Cauchy kernel
We study the exceptional case of the characteristic singular integral equation with Cauchy kernel in which its coefficients admit zeros or singularities of complex orders at finitely many points of the contour. By reduction to a linear conjugation problem, we obtain an explicit solution formula and solvability conditions for this equation in weighted Hölder classes
Anderson-Yuval approach to the multichannel Kondo problem
We analyze the structure of the perturbation expansion of the general
multichannel Kondo model with channel anisotropic exchange couplings and in the
presence of an external magnetic field, generalizing to this case the
Anderson-Yuval technique. For two channels, we are able to map the Kondo model
onto a generalized resonant level model. Limiting cases in which the equivalent
resonant level model is solvable are identified. The solution correctly
captures the properties of the two channel Kondo model, and also allows an
analytic description of the cross-over from the non Fermi liquid to the Fermi
liquid behavior caused by the channel anisotropy.Comment: 23 pages, ReVTeX, 4 figures av. on reques
Elliptic equations, manifolds with non-smooth boundaries, and boundary value problems
We discuss basic principles for constructing the theory of boundary value problems on manifolds with non-smooth boundaries. It includes studying local situations related to model pseudo-differential equations in canonical domains. The technique consists of Fourier transform, multi-dimensional Riemann boundary value problem, wave factorization, and multi-variable complex analysi
Solving Open String Field Theory with Special Projectors
Schnabl recently found an analytic expression for the string field tachyon
condensate using a gauge condition adapted to the conformal frame of the sliver
projector. We propose that this construction is more general. The sliver is an
example of a special projector, a projector such that the Virasoro operator
\L_0 and its BPZ adjoint \L*_0 obey the algebra [\L_0, \L*_0] = s (\L_0 +
\L*_0), with s a positive real constant. All special projectors provide abelian
subalgebras of string fields, closed under both the *-product and the action of
\L_0. This structure guarantees exact solvability of a ghost number zero string
field equation. We recast this infinite recursive set of equations as an
ordinary differential equation that is easily solved. The classification of
special projectors is reduced to a version of the Riemann-Hilbert problem, with
piecewise constant data on the boundary of a disk.Comment: 64 pages, 6 figure
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