1,403 research outputs found
Exact Casimir Interaction Between Semitransparent Spheres and Cylinders
A multiple scattering formulation is used to calculate the force, arising
from fluctuating scalar fields, between distinct bodies described by
-function potentials, so-called semitransparent bodies. (In the limit
of strong coupling, a semitransparent boundary becomes a Dirichlet one.) We
obtain expressions for the Casimir energies between disjoint parallel
semitransparent cylinders and between disjoint semitransparent spheres. In the
limit of weak coupling, we derive power series expansions for the energy, which
can be exactly summed, so that explicit, very simple, closed-form expressions
are obtained in both cases. The proximity force theorem holds when the objects
are almost touching, but is subject to large corrections as the bodies are
moved further apart.Comment: 5 pages, 4 eps figures; expanded discussion of previous work and
additional references added, minor typos correcte
Positivity and optimization for semi-algebraic functions
We describe algebraic certificates of positivity for functions belonging to a
finitely generated algebra of Borel measurable functions, with particular
emphasis to algebras generated by semi-algebraic functions. In which case the
standard global optimization problem with constraints given by elements of the
same algebra is reduced via a natural change of variables to the better
understood case of polynomial optimization. A collection of simple examples and
numerical experiments complement the theoretical parts of the article.Comment: 20 page
Cosmic Strings Stabilized by Fermion Fluctuations
We provide a thorough exposition of recent results on the quantum
stabilization of cosmic strings. Stabilization occurs through the coupling to a
heavy fermion doublet in a reduced version of the standard model. The study
combines the vacuum polarization energy of fermion zero-point fluctuations and
the binding energy of occupied energy levels, which are of the same order in a
semi-classical expansion. Populating these bound states assigns a charge to the
string. Strings carrying fermion charge become stable if the Higgs and gauge
fields are coupled to a fermion that is less than twice as heavy as the top
quark. The vacuum remains stable in the model, because neutral strings are not
energetically favored. These findings suggest that extraordinarily large
fermion masses or unrealistic couplings are not required to bind a cosmic
string in the standard model.Comment: Based on talk by HW at QFEXT 11 (Benasque, Spain), 15p, uses
ws-ijmpcs.cls (incl
Applications of M.G. Krein's Theory of Regular Symmetric Operators to Sampling Theory
The classical Kramer sampling theorem establishes general conditions that
allow the reconstruction of functions by mean of orthogonal sampling formulae.
One major task in sampling theory is to find concrete, non trivial realizations
of this theorem. In this paper we provide a new approach to this subject on the
basis of the M. G. Krein's theory of representation of simple regular symmetric
operators having deficiency indices (1,1). We show that the resulting sampling
formulae have the form of Lagrange interpolation series. We also characterize
the space of functions reconstructible by our sampling formulae. Our
construction allows a rigorous treatment of certain ideas proposed recently in
quantum gravity.Comment: 15 pages; v2: minor changes in abstract, addition of PACS numbers,
changes in some keywords, some few changes in the introduction, correction of
the proof of the last theorem, and addition of some comments at the end of
the fourth sectio
Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials
We give a complete description of the set of spectral data (eigenvalues and
specially introduced norming constants) for Sturm--Liouville operators on the
interval with matrix-valued potentials in the Sobolev space
and suggest an algorithm reconstructing the potential from the spectral data
that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO
The class of n-entire operators
We introduce a classification of simple, regular, closed symmetric operators
with deficiency indices (1,1) according to a geometric criterion that extends
the classical notions of entire operators and entire operators in the
generalized sense due to M. G. Krein. We show that these classes of operators
have several distinctive properties, some of them related to the spectra of
their canonical selfadjoint extensions. In particular, we provide necessary and
sufficient conditions on the spectra of two canonical selfadjoint extensions of
an operator for it to belong to one of our classes. Our discussion is based on
some recent results in the theory of de Branges spaces.Comment: 33 pages. Typos corrected. Changes in the wording of Section 2.
References added. Examples added. arXiv admin note: text overlap with
arXiv:1104.476
Symmetry-preserving contact interaction model for heavy-light mesons
We use a symmetry-preserving regularization method of ultraviolet divergences
in a vector-vector contact interac- tion model for low-energy QCD. The contact
interaction is a representation of nonperturbative kernels used Dyson-Schwinger
and Bethe-Salpeter equations. The regularization method is based on a
subtraction scheme that avoids standard steps in the evaluation of divergent
integrals that invariably lead to symmetry violation. Aiming at the study of
heavy-light mesons, we have implemented the method to the pseudoscalar pion and
Kaon mesons. We have solved the Dyson-Schwinger equation for the u, d and s
quark propagators, and obtained the bound-state Bethe-Salpeter amplitudes in a
way that the Ward-Green-Takahashi identities reflecting global symmetries of
the model are satisfied for arbitrary routing of the momenta running in loop
integrals
Bounds for mixing time of quantum walks on finite graphs
Several inequalities are proved for the mixing time of discrete-time quantum
walks on finite graphs. The mixing time is defined differently than in
Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for
particular examples of walks on a cycle, a hypercube and a complete graph,
quantum walks provide no speed-up in mixing over the classical counterparts. In
addition, non-unitary quantum walks (i.e., walks with decoherence) are
considered and a criterion for their convergence to the unique stationary
distribution is derived.Comment: This is the journal version (except formatting); it is a significant
revision of the previous version, in particular, it contains a new result
about the convergence of quantum walks with decoherence; 16 page
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