4,766 research outputs found
Extended symmetrical classical electrodynamics
In the present article, we discuss a modification of classical
electrodynamics in which ``ordinary'' point charges are absent. The modified
equations contain additional terms describing the induced charges and currents.
The densities of the induced charges and currents depend on the vector k and
the vectors of the electromagnetic field E and B. It is shown that the vectors
E and B can be defined in terms of two 4-potentials and the components of k are
the components of the 4-tensor of the third rank. The Lagrangian of modified
electrodynamics is defined. The conditions are derived at which only one
4-potential determines the behavior of the electromagnetic field. It is also
shown that static modified electrodynamics can describe the electromagnetic
field in the inner region of the electric monopole. In the outer region of the
electric monopole the electric field is governed by the Maxwell equations. It
follows from boundary conditions at the interface between the inner and outer
regions of the monopole that the vector k has a discrete spectrum. The electric
and magnetic fields, energy and angular momentum of the monopole are found for
different eigenvalues of k
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
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.
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
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
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