2,922 research outputs found
Asymptotic behavior in time periodic parabolic problems with unbounded coefficients
We study asymptotic behavior in a class of non-autonomous second order
parabolic equations with time periodic unbounded coefficients in . Our results generalize and improve asymptotic behavior
results for Markov semigroups having an invariant measure. We also study
spectral properties of the realization of the parabolic operator in suitable spaces
Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations
We consider a class of nonautonomous second order parabolic equations with
unbounded coefficients defined in , where is a right-halfline.
We prove logarithmic Sobolev and Poincar\'e inequalities with respect to an
associated evolution system of measures , and we deduce
hypercontractivity and asymptotic behaviour results for the evolution operator
Distributional approach to point interactions in one-dimensional quantum mechanics
We consider the one-dimensional quantum mechanical problem of defining
interactions concentrated at a single point in the framework of the theory of
distributions. The often ill-defined product which describes the interaction
term in the Schr\"odinger and Dirac equations is replaced by a well-defined
distribution satisfying some simple mathematical conditions and, in addition,
the physical requirement of probability current conservation is imposed. A
four-parameter family of interactions thus emerges as the most general point
interaction both in the non-relativistic and in the relativistic theories (in
agreement with results obtained by self-adjoint extensions). Since the
interaction is given explicitly, the distributional method allows one to carry
out symmetry investigations in a simple way, and it proves to be useful to
clarify some ambiguities related to the so-called interaction.Comment: Open Access link:
http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00023/abstrac
Gauged Thirring Model in the Heisenberg Picture
We consider the (2+1)-dimensional gauged Thirring model in the Heisenberg
picture. In this context we evaluate the vacuum polarization tensor as well as
the corrected gauge boson propagator and address the issues of generation of
mass and dynamics for the gauge boson (in the limits of QED and Thirring
model as a gauge theory, respectively) due to the radiative corrections.Comment: 14 pages, LaTex, no figure
Spin 1 fields in Riemann-Cartan space-times "via" Duffin-Kemmer-Petiau theory
We consider massive spin 1 fields, in Riemann-Cartan space-times, described
by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling
between the spin 1 field and the space-time torsion which breaks the usual
equivalence with the Proca theory, but that such equivalence is preserved in
the context of the Teleparallel Equivalent of General Relativity.Comment: 8 pages, no figures, revtex. Dedicated to Professor Gerhard Wilhelm
Bund on the occasion of his 70th birthday. To appear in Gen. Rel. Grav.
Equations numbering corrected. References update
Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces
We prove a Miyadera-Voigt type perturbation theorem for strong Feller
semigroups. Using this result, we prove well-posedness of the semilinear
stochastic equation dX(t) = [AX(t) + F(X(t))]dt + GdW_H(t) on a separable
Banach space E, assuming that F is bounded and measurable and that the
associated linear equation, i.e. the equation with F = 0, is well-posed and its
transition semigroup is strongly Feller and satisfies an appropriate gradient
estimate. We also study existence and uniqueness of invariant measures for the
associated transition semigroup.Comment: Revision based on the referee's comment
Relativistic Tunneling Through Two Successive Barriers
We study the relativistic quantum mechanical problem of a Dirac particle
tunneling through two successive electrostatic barriers. Our aim is to study
the emergence of the so-called \emph{Generalized Hartman Effect}, an effect
observed in the context of nonrelativistic tunneling as well as in its
electromagnetic counterparts, and which is often associated with the
possibility of superluminal velocities in the tunneling process. We discuss the
behavior of both the phase (or group) tunneling time and the dwell time, and
show that in the limit of opaque barriers the relativistic theory also allows
the emergence of the Generalized Hartman Effect. We compare our results with
the nonrelativistic ones and discuss their interpretation.Comment: 7 pages, 3 figures. Revised version, with a new appendix added.
Slightly changes in the styles and captions of Figures 1 and 2. To appear in
Physical Review
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