543 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
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
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
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
Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD
We consider a benchmark bulk theory in four-dimensions: N=2 supersymmetric
QCD with the gauge group U(N) and N_f flavors of fundamental matter
hypermultiplets (quarks). The nature of the BPS strings in this benchmark
theory crucially depends on N_f. If N_f\geq N and all quark masses are equal,
it supports non-Abelian BPS strings which have internal (orientational) moduli.
If N_f>N these strings become semilocal, developing additional moduli \rho
related to (unlimited) variations of their transverse size.
Using the U(2) gauge group with N_f=3,4 as an example, we derive an effective
low-energy theory on the (two-dimensional) string world sheet. Our derivation
is field-theoretic, direct and explicit: we first analyze the Bogomol'nyi
equations for string-geometry solitons, suggest an ansatz and solve it at large
\rho. Then we use this solution to obtain the world-sheet theory.
In the semiclassical limit our result confirms the Hanany-Tong conjecture,
which rests on brane-based arguments, that the world-sheet theory is N=2
supersymmetric U(1) gauge theory with N positively and N_e=N_f-N negatively
charged matter multiplets and the Fayet-Iliopoulos term determined by the
four-dimensional coupling constant. We conclude that the Higgs branch of this
model is not lifted by quantum effects. As a result, such strings cannot
confine.
Our analysis of infrared effects, not seen in the Hanany-Tong consideration,
shows that, in fact, the derivative expansion can make sense only provided the
theory under consideration is regularized in the infrared, e.g. by the quark
mass differences. The world-sheet action discussed in this paper becomes a bona
fide low-energy effective action only if \Delta m_{AB}\neq 0.Comment: 36 pages, no figure
Nearest-neighbor distribution for singular billiards
The exact computation of the nearest-neighbor spacing distribution P(s) is
performed for a rectangular billiard with point-like scatterer inside for
periodic and Dirichlet boundary conditions and it is demonstrated that for
large s this function decreases exponentially. Together with the results of
[Bogomolny et al., Phys. Rev. E 63, 036206 (2001)] it proves that spectral
statistics of such systems is of intermediate type characterized by level
repulsion at small distances and exponential fall-off of the nearest-neighbor
distribution at large distances. The calculation of the n-th nearest-neighbor
spacing distribution and its asymptotics is performed as well for any boundary
conditions.Comment: 38 pages, 10 figure
Multifractal dimensions for all moments for certain critical random matrix ensembles in the strong multifractality regime
We construct perturbation series for the q-th moment of eigenfunctions of
various critical random matrix ensembles in the strong multifractality regime
close to localization. Contrary to previous investigations, our results are
valid in the region q<1/2. Our findings allow to verify, at first leading
orders in the strong multifractality limit, the symmetry relation for anomalous
fractal dimensions Delta(q)=Delta(1-q), recently conjectured for critical
models where an analogue of the metal-insulator transition takes place. It is
known that this relation is verified at leading order in the weak
multifractality regime. Our results thus indicate that this symmetry holds in
both limits of small and large coupling constant. For general values of the
coupling constant we present careful numerical verifications of this symmetry
relation for different critical random matrix ensembles. We also present an
example of a system closely related to one of these critical ensembles, but
where the symmetry relation, at least numerically, is not fulfilled.Comment: 12 pages, 12 figure
Electromagnetic Interaction in the System of Multimonopoles and Vortex Rings
Behavior of static axially symmetric monopole-antimonopole and vortex ring
solutions of the SU(2) Yang-Mills-Higgs theory in an external uniform magnetic
field is considered. It is argued that the axially symmetric
monopole-antimonopole chains and vortex rings can be treated as a bounded
electromagnetic system of the magnetic charges and the electric current rings.
The magnitude of the external field is a parameter which may be used to test
the structure of the static potential of the effective electromagnetic
interaction between the monopoles with opposite orientation in the group space.
It is shown that for a non-BPS solutions there is a local minimum of this
potential.Comment: 10 pages, 12 figures, some minor corrections, version to appear in
Phys. Rev.
Semi-classical analysis of real atomic spectra beyond Gutzwiller's approximation
Real atomic systems, like the hydrogen atom in a magnetic field or the helium
atom, whose classical dynamics are chaotic, generally present both discrete and
continuous symmetries. In this letter, we explain how these properties must be
taken into account in order to obtain the proper (i.e. symmetry projected)
expansion of semiclassical expressions like the Gutzwiller trace
formula. In the case of the hydrogen atom in a magnetic field, we shed light on
the excellent agreement between present theory and exact quantum results.Comment: 4 pages, 1 figure, final versio
Det-Det Correlations for Quantum Maps: Dual Pair and Saddle-Point Analyses
An attempt is made to clarify the ballistic non-linear sigma model formalism
recently proposed for quantum chaotic systems, by the spectral determinant
Z(s)=Det(1-sU) of a quantized map U element of U(N). More precisely, we study
the correlator omega_U(s)= (averaging t over the unit circle).
Identifying the group U(N) as one member of a dual pair acting in the spinor
representation of Spin(4N), omega_U(s) is expanded in terms of irreducible
characters of U(N). In close analogy with the ballistic non-linear sigma model,
a coherent-state integral representation of omega_U(s) is developed. We show
that the leading-order saddle-point approximation reproduces omega_U(s)
exactly, up to a constant factor; this miracle can be explained by interpreting
omega_U(s) as a character of U(2N), for which the saddle-point expansion yields
the Weyl character formula. Unfortunately, this decomposition behaves
non-smoothly in the semiclassical limit, and to make further progress some
averaging over U needs to be introduced. Several averaging schemes are
investigated. In general, a direct application of the saddle-point
approximation to these schemes is demonstrated to give incorrect results; this
is not the case for a `semiclassical averaging scheme', for which all loop
corrections vanish identically. As a side product of the dual pair
decomposition, we compute a crossover between the Poisson and CUE ensembles for
omega_U(s)
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