3,853 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
Experimental Monte Carlo Quantum Process Certification
Experimental implementations of quantum information processing have now
reached a level of sophistication where quantum process tomography is
impractical. The number of experimental settings as well as the computational
cost of the data post-processing now translates to days of effort to
characterize even experiments with as few as 8 qubits. Recently a more
practical approach to determine the fidelity of an experimental quantum process
has been proposed, where the experimental data is compared directly to an ideal
process using Monte Carlo sampling. Here we present an experimental
implementation of this scheme in a circuit quantum electrodynamics setup to
determine the fidelity of two qubit gates, such as the cphase and the cnot
gate, and three qubit gates, such as the Toffoli gate and two sequential cphase
gates
Three-Body Halos in Two Dimensions
A method to study weakly bound three-body quantum systems in two dimensions
is formulated in coordinate space for short-range potentials. Occurrences of
spatially extended structures (halos) are investigated. Borromean systems are
shown to exist in two dimensions for a certain class of potentials. An
extensive numerical investigation shows that a weakly bound two-body state
gives rise to two weakly bound three-body states, a reminiscence of the Efimov
effect in three dimensions. The properties of these two states in the weak
binding limit turn out to be universal.
PACS number(s): 03.65.Ge, 21.45.+v, 31.15.Ja, 02.60NmComment: 9 pages, 2 postscript figures, LaTeX, epsf.st
On calculating the Berry curvature of Bloch electrons using the KKR method
We propose and implement a particularly effective method for calculating the
Berry curvature arising from adiabatic evolution of Bloch states in wave vector
k space. The method exploits a unique feature of the Korringa-Kohn-Rostoker
(KKR) approach to solve the Schr\"odinger or Dirac equations. Namely, it is
based on the observation that in the KKR method k enters the calculation via
the structure constants which depend only on the geometry of the lattice but
not the crystal potential. For both the Abelian and non-Abelian Berry curvature
we derive an analytic formula whose evaluation does not require any numerical
differentiation with respect to k. We present explicit calculations for Al, Cu,
Au, and Pt bulk crystals.Comment: 13 pages, 5 figure
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.
Spectral and polarization effects in deterministically nonperiodic multilayers containing optically anisotropic and gyrotropic materials
Influence of material anisotropy and gyrotropy on optical properties of
fractal multilayer nanostructures is theoretically investigated. Gyrotropy is
found to uniformly rotate the output polarization for bi-isotropic multilayers
of arbitrary geometrical structure without any changes in transmission spectra.
When introduced in a polarization splitter based on a birefringent fractal
multilayer, isotropic gyrotropy is found to resonantly alter output
polarizations without shifting of transmission peak frequencies. The design of
frequency-selective absorptionless polarizers for polarization-sensitive
integrated optics is outlined
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
Packet narrowing and quantum entanglement in photoionization and photodissociation
The narrowing of electron and ion wave packets in the process of
photoionization is investigated, with the electron-ion recoil fully taken into
account. Packet localization of this type is directly related to entanglement
in the joint quantum state of electron and ion, and to Einstein-Podolsky-Rosen
localization. Experimental observation of such packet-narrowing effects is
suggested via coincidence registration by two detectors, with a fixed position
of one and varying position of the other. A similar effect, typically with an
enhanced degree of entanglement, is shown to occur in the case of
photodissociation of molecules
Comparing Local Fitting to Other Automatic Smoothers
In a public service enterprise by Breiman and Peters (1991) various automatic smoothers, such as the supersmoother (SSMU), cross-validated smoothing splines (BART), delete-knot regression splines (DKS) and the cross-validated kernel smooth (KERNEL) were compared by simulation on a variety of sample sizes, noise levels and functions. The intention was to give practitioners guidelines when to use which type of smoother. The given work completes those simulations by including the increasingly popular local fitting approach, that was introduced to the statistical literature by Cleveland (1979). Fedorov et al. (1993) have modified the technique in order to take account possible misspecification bias, termed 'optimized moving local regression', and here we use an automated version (by crossvalidation) of it as given in Fedorov et al. (1994). (author's abstract)Series: Forschungsberichte / Institut fĂĽr Statisti
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