3,879 research outputs found
Upper bounds for the number of orbital topological types of planar polynomial vector fields "modulo limit cycles"
The paper deals with planar polynomial vector fields. We aim to estimate the
number of orbital topological equivalence classes for the fields of degree n.
An evident obstacle for this is the second part of Hilbert's 16th problem. To
circumvent this obstacle we introduce the notion of equivalence modulo limit
cycles. This paper is the continuation of the author's paper in [Mosc. Math. J.
1 (2001), no. 4] where the lower bound of the form 2^{cn^2} has been obtained.
Here we obtain the upper bound of the same form. We also associate an equipped
planar graph to every planar polynomial vector field, this graph is a complete
invariant for orbital topological classification of such fields.Comment: 23 pages, 5 figure
Momentum Distributions of Particles from Three--Body Halo Fragmentation: Final State Interactions
Momentum distributions of particles from nuclear break-up of fast three-body
halos are calculated consistently, and applied to Li. The same two-body
interactions between the three particles are used to calculate the ground state
structure and the final state of the reaction processes. We reproduce the
available momentum distributions from Li fragmentation, together with
the size and energy of Li, with a neutron-core relative state containing
a -state admixture of 20\%-30\%. The available fragmentation data strongly
suggest an -state in Li at about 50 keV, and indicate a -state
around 500 keV.Comment: 11 pages (RevTeX), 3 Postscript figures (uuencoded postscript file
attached at the end of the LaTeX file). To be published in Phys. Rev.
Phase diagram analysis and crystal growth of solid solutions Ca_{1-x}Sr_xF_2
The binary phase diagram CaF--SrF was investigated by differential
thermal analysis (DTA). Both substances exhibit unlimited mutual solubility
with an azeotropic point showing a minimum melting temperature of
T_\mathrm{min}=1373^{\circ}_{0.582}_{0.418}_2$. Close to this composition, homogeneous single
crystals up to 30 mm diameter without remarkable segregation could be grown by
the Czochralski method.Comment: accepted for publication in J. Crystal Growt
Local Phonon Density of States in an Elastic Substrate
The local, eigenfunction-weighted acoustic phonon density of states (DOS)
tensor is calculated for a model substrate consisting of a semi-infinite
isotropic elastic continuum with a stress-free surface. On the surface, the
local DOS is proportional to the square of the frequency, as for the
three-dimensional Debye model, but with a constant of proportionality that is
considerably enhanced compared to the Debye value, a consequence of the
Rayleigh surface modes. The local DOS tensor at the surface is also
anisotropic, as expected. Inside the substrate the local DOS is both spatially
anisotropic and non-quadratic in frequency. However, at large depths, the local
DOS approaches the isotropic Debye value. The results are applied to a Si
substrate.Comment: 7 pages, 2 figures, RevTe
Computations of Three-Body Continuum Spectra
We formulate a method to solve the coordinate space Faddeev equations for
positive energies. The method employs hyperspherical coordinates and analytical
expressions for the effective potentials at large distances. Realistic
computations of the parameters of the resonances and the strength functions are
carried out for the Borromean halo nucleus 6He (n+n+alpha) for J = 0+, 0-, 1+,
1-, 2+,2-. PACS numbers: 21.45.+v, 11.80.Jy, 31.15.Ja, 21.60.GxComment: 10 pages, 3 postscript figures, LaTeX, epsf.sty, corrected misprints
in the caption of Fig.
The structure of the atomic helium trimers: Halos and Efimov states
The Faddeev equations for the atomic helium-trimer systems are solved
numerically with high accuracy both for the most sophisticated realistic
potentials available and for simple phenomenological potentials. An efficient
numerical procedure is described. The large-distance asymptotic behavior,
crucial for weakly bound three-body systems, is described almost analytically
for arbitrary potentials. The Efimov effect is especially considered. The
geometric structures of the bound states are quantitatively investigated. The
accuracy of the schematic models and previous computations is comparable, i.e.
within 20% for the spatially extended states and within 40% for the smaller
^4He-trimer ground state.Comment: 32 pages containing 7 figures and 6 table
Confluent primary fields in the conformal field theory
For any complex simple Lie algebra, we generalize primary fileds in the
Wess-Zumino-Novikov-Witten conformal field theory with respect to the case of
irregular singularities and we construct integral representations of
hypergeometric functions of confluent type, as expectation values of products
of generalized primary fields. In the case of sl(2), these integral
representations coincide with solutions to confluent KZ equations. Computing
the operator product expansion of the energy-momentum tensor and the
generalized primary field, new differential operators appear in the result. In
the case of sl(2), these differential operators are the same as those of the
confluent KZ equations.Comment: 15 pages. Corrected typos. Proposition 3.1 rewritten. Other minor
changes, title change
Chemically gated electronic structure of a superconducting doped topological insulator system
Angle resolved photoemission spectroscopy is used to observe changes in the
electronic structure of bulk-doped topological insulator CuBiSe as
additional copper atoms are deposited onto the cleaved crystal surface. Carrier
density and surface-normal electrical field strength near the crystal surface
are estimated to consider the effect of chemical surface gating on atypical
superconducting properties associated with topological insulator order, such as
the dynamics of theoretically predicted Majorana Fermion vortices
Bound states of Dipolar Bosons in One-dimensional Systems
We consider one-dimensional tubes containing bosonic polar molecules. The
long-range dipole-dipole interactions act both within a single tube and between
different tubes. We consider arbitrary values of the externally aligned dipole
moments with respect to the symmetry axis of the tubes. The few-body structures
in this geometry are determined as function of polarization angles and dipole
strength by using both essentially exact stochastic variational methods and the
harmonic approximation. The main focus is on the three, four, and five-body
problems in two or more tubes. Our results indicate that in the weakly-coupled
limit the inter-tube interaction is similar to a zero-range term with a
suitable rescaled strength. This allows us to address the corresponding
many-body physics of the system by constructing a model where bound chains with
one molecule in each tube are the effective degrees of freedom. This model can
be mapped onto one-dimensional Hamiltonians for which exact solutions are
known.Comment: 22 pages, 7 figures, revised versio
Cluster sum rules for three-body systems with angular-momentum dependent interactions
We derive general expressions for non-energy weighted and energy-weighted
cluster sum rules for systems of three charged particles. The interferences
between pairs of particles are found to play a substantial role. The
energy-weighted sum rule is usually determined by the kinetic energy operator,
but we demonstrate that it has similar additional contributions from the
angular momentum and parity dependence of two- and three-body potentials
frequently used in three-body calculations. The importance of the different
contributions is illustrated with the dipole excitations in He. The results
are compared with the available experimental data.Comment: 11 pages, 3 figures, 2 table
- …