40,370 research outputs found
On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background
The problem of spin-0 and spin-1 bosons in the background of a general mixing
of minimal and nonminimal vector inversely linear potentials is explored in a
unified way in the context of the Duffin-Kemmer-Petiau theory. It is shown that
spin-0 and spin-1 bosons behave effectively in the same way. An orthogonality
criterion is set up and it is used to determine uniquely the set of solutions
as well as to show that even-parity solutions do not exist.Comment: 10 page
The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps
We probe deeper into the Discrete Markus-Yamabe Question for polynomial
planar maps and into the normal form for those maps which answer this question
in the affirmative. Furthermore, in a symmetric context, we show that the only
nonlinear equivariant polynomial maps providing an affirmative answer to the
Discrete Markus-Yamabe Question are those possessing Z2 as their group of
symmetries. We use this to establish two new tools which give information about
the spectrum of a planar polynomial map
Global Saddles for Planar Maps
We study the dynamics of planar diffeomorphisms having a unique fixed point
that is a hyperbolic local saddle. We obtain sufficient conditions under which
the fixed point is a global saddle. We also address the special case of
-symmetric maps, for which we obtain a similar result for
homeomorphisms. Some applications to differential equations are also given
Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials
The Klein-Gordon and the Dirac equations with vector and scalar potentials
are investigated under a more general condition, . These intrinsically relativistic and isospectral problems
are solved in a case of squared hyperbolic potential functions and bound states
for either particles or antiparticles are found. The eigenvalues and
eigenfuntions are discussed in some detail and the effective Compton wavelength
is revealed to be an important physical quantity. It is revealed that a boson
is better localized than a fermion when they have the same mass and are
subjected to the same potentials.Comment: 3 figure
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