93 research outputs found
The Kink variety in systems of two coupled scalar fields in two space-time dimensions
In this paper we describe the moduli space of kinks in a class of systems of
two coupled real scalar fields in (1+1) Minkowskian space-time. The main
feature of the class is the spontaneous breaking of a discrete symmetry of
(real) Ginzburg-Landau type that guarantees the existence of kink topological
defects.Comment: 12 pages, 5 figures. To appear in Phys. Rev.
Factorization of supersymmetric Hamiltonians in curvilinear coordinates
Planar supersymmetric quantum mechanical systems with separable spectral
problem in curvilinear coordinates are analyzed in full generality. We
explicitly construct the supersymmetric extension of the Euler/Pauli
Hamiltonian describing the motion of a light particle in the field of two heavy
fixed Coulombian centers. We shall also show how the SUSY Kepler/Coulomb
problem arises in two different limits of this problem: either, the two centers
collapse in one center - a problem separable in polar coordinates -, or, one of
the two centers flies to infinity - to meet the Coulomb problem separable in
parabolic coordinates.Comment: 13 pages. Based on the talk presented by M.A. Gonzalez Leon at the
7th International Conference on Quantum Theory and Symmetries (QTS7), August
07-13, 2011, Prague, Czech Republi
Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
The problem of building supersymmetry in the quantum mechanics of two
Coulombian centers of force is analyzed. It is shown that there are essentially
two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians
are quite similar and become tantamount to solving entangled families of Razavy
and Whittaker-Hill equations in the first approach. When the two centers have
the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In
the second approach, the spectral problems are much more difficult to solve but
one can still find the zero-energy ground states.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Constructing networks of defects with scalar fields
We propose a new way to build networks of defects. The idea takes advantage
of the deformation procedure recently employed to describe defect structures,
which we use to construct networks, spread from small rudimentary networks that
appear in simple models of scalar fields.Comment: 5 pages, 4 figures, version with new title, motivations and
references, to appear in PL
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