362 research outputs found
generalized Robin boundary conditions and quantum vacuum fluctuations
The effects induced by the quantum vacuum fluctuations of one massless real
scalar field on a configuration of two partially transparent plates are
investigated. The physical properties of the infinitely thin plates are
simulated by means of Dirac- point interactions. It is
shown that the distortion caused on the fluctuations by this external
background gives rise to a generalization of Robin boundary conditions. The
-operator for potentials concentrated on points with non defined parity is
computed with total generality. The quantum vacuum interaction energy between
the two plates is computed using the formula to find positive, negative,
and zero Casimir energies. The parity properties of the
potential allow repulsive quantum vacuum force between identical plates.Comment: 21 pages and 11 figures. PhysRev
Quantum scalar fields in the half-line. A heat kernel/zeta function approach
In this paper we shall study vacuum fluctuations of a single scalar field
with Dirichlet boundary conditions in a finite but very long line. The spectral
heat kernel, the heat partition function and the spectral zeta function are
calculated in terms of Riemann Theta functions, the error function, and
hypergeometric PFQ functions.Comment: Latex file, 11 pages, 7 figure
Two-point one-dimensional - interactions: non-abelian addition law and decoupling limit
In this contribution to the study of one dimensional point potentials, we
prove that if we take the limit on a potential of the type
, we
obtain a new point potential of the type , when and are related to , , and
by a law having the structure of a group. This is the Borel subgroup of
. We also obtain the non-abelian addition law from the
scattering data. The spectra of the Hamiltonian in the exceptional cases
emerging in the study are also described in full detail. It is shown that for
the , values of the couplings the
singular Kurasov matrices become equivalent to Dirichlet at one side of the
point interaction and Robin boundary conditions at the other side
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.
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
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