597 research outputs found

### Asymptotic behaviour of multiple scattering on infinite number of parallel demi-planes

The exact solution for the scattering of electromagnetic waves on an infinite
number of parallel demi-planes has been obtained by J.F. Carlson and A.E. Heins
in 1947 using the Wiener-Hopf method. We analyze their solution in the
semiclassical limit of small wavelength and find the asymptotic behaviour of
the reflection and transmission coefficients. The results are compared with the
ones obtained within the Kirchhoff approximation

### Strings in Yang-Mills-Higgs theory coupled to gravity

Non-Abelian strings for an Einstein-Yang-Mills-Higgs theory are explicitly
constructed. We consider N_f Higgs fields in the fundamental representation of
the U(1)xSU(N_c) gauge group in order to have a color-flavor SU(N_c) group
remaining unbroken. Choosing a suitable ansatz for the metric, Bogomol'nyi-like
first order equations are found and rotationally symmetric solutions are
proposed. In the N_f = N_c case, solutions are local strings and are shown to
be truly non-Abelian by parameterizing them in terms of orientational
collective coordinates. When N_f > N_c, the solutions correspond to semilocal
strings which, beside the orientational degrees of freedom, acquire additional
collective coordinates parameterizing their transverse size. The low-energy
effective theories for the correspondent moduli are found, showing that all
zero modes are normalizable in presence of gravity, even in the semilocal case.Comment: 20 pages, no figure, modified version with new title, abstract and an
additional section completing the study of effective theories. Physical
Review D in pres

### Semi-classical calculations of the two-point correlation form factor for diffractive systems

The computation of the two-point correlation form factor K(t) is performed
for a rectangular billiard with a small size impurity inside for both periodic
or Dirichlet boundary conditions. It is demonstrated that all terms of
perturbation expansion of this form factor in powers of t can be computed
directly by semiclassical trace formula. The main part of the calculation is
the summation of non-diagonal terms in the cross product of classical orbits.
When the diffraction coefficient is a constant our results coincide with
expansion of exact expressions ontained by a different method.Comment: 42 pages, 10 figures, Late

### Spectral density of the quantum Ising model in two fields: Gaussian and multi-Gaussian approximations

Spectral density of quantum Ising model in two fields for large but finite
number of spins $N$, is discussed in detail. When all coupling constants are of
the same order, spectral densities in the bulk are well approximated by a
Gaussian function which is typical behaviour for many-body models with
short-range interactions. The main part of the paper is devoted to the
investigation of a different characteristic case when spectral densities have
peaks related with strong degeneracies of unperturbed states in certain limits
of coupling constants. In the strict limit $N\to\infty$, peaks overlap and
disappear but for values of $N$ accessible in numerical calculations they often
strongly influence spectral densities and other quantities as well. A simple
method is developed which permits to find general approximation formulae for
multi-peak structure of spectral density in good agreement with numerics.Comment: 32 pages, 13 figure

### Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime

The power-law random banded matrices and the ultrametric random matrices are
investigated numerically in the regime where eigenstates are extended but all
integer matrix moments remain finite in the limit of large matrix dimensions.
Though in this case standard analytical tools are inapplicable, we found that
in all considered cases eigenvector distributions are extremely well described
by the generalised hyperbolic distribution which differs considerably from the
usual Porter-Thomas distribution but shares with it certain universal
properties.Comment: 20 pages, 12 figure

### Trace formula for dielectric cavities III: TE modes

The construction of the semiclassical trace formula for the resonances with
the transverse electric (TE) polarization for two-dimensional dielectric
cavities is discussed. Special attention is given to the derivation of the two
first terms of Weyl's series for the average number of such resonances. The
obtained formulas agree well with numerical calculations for dielectric
cavities of different shapes.Comment: 12 pages, 6 figure

### Composite non-Abelian Flux Tubes in N=2 SQCD

Composite non-Abelian vortices in N=2 supersymmetric U(2) SQCD are
investigated. The internal moduli space of an elementary non-Abelian vortex is
CP^1. In this paper we find a composite state of two coincident non-Abelian
vortices explicitly solving the first order BPS equations. Topology of the
internal moduli space T is determined in terms of a discrete quotient CP^2/Z_2.
The spectrum of physical strings and confined monopoles is discussed.
This gives indirect information about the sigma model with target space T.Comment: 37 pages, 7 figures, v3 details added, v4 erratum adde

### Axially Symmetric Solutions for SU(2) Yang-Mills Theory

By casting the Yang-Mills-Higgs equations of an SU(2) theory in the form of
the Ernst equations of general relativity, it is shown how the known exact
solutions of general relativity can be used to give similiar solutions for
Yang-Mills theory. Thus all the known exact solutions of general relativity
with axial symmetry (e.g. the Kerr metric, the Tomimatsu-Sato metric) have
Yang-Mills equivalents. In this paper we only examine in detail the Kerr-like
solution. It will be seen that this solution has surfaces where the gauge and
scalar fields become infinite, which correspond to the infinite redshift
surfaces of the normal Kerr solution. It is speculated that this feature may be
connected with the confinement mechanism since any particle which carries an
SU(2) color charge would tend to become trapped once it passes these surfaces.
Unlike the Kerr solution, our solution apparently does not have any intrinsic
angular momentum, but rather appears to give the non-Abelian field
configuration associated with concentric shells of color charge.Comment: 15 pages LaTe

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