98,783 research outputs found
Regularity of Eigenstates in Regular Mourre Theory
The present paper gives an abstract method to prove that possibly embedded
eigenstates of a self-adjoint operator lie in the domain of the
power of a conjugate operator . Conjugate means here that and have a
positive commutator locally near the relevant eigenvalue in the sense of
Mourre. The only requirement is regularity of . Regarding
integer , our result is optimal. Under a natural boundedness assumption of
the multiple commutators we prove that the eigenstate 'dilated' by
is analytic in a strip around the real axis. In particular,
the eigenstate is an analytic vector with respect to . Natural applications
are 'dilation analytic' systems satisfying a Mourre estimate, where our result
can be viewed as an abstract version of a theorem due to Balslev and Combes. As
a new application we consider the massive Spin-Boson Model.Comment: 27 page
A graph theoretical analysis of certain aspects of Bahasa Indonesia
In this paper the theory of knowledge graphs is applied to some characteristic features of the Indonesian language. The characteristic features to be considered are active and passive form of verbs and the derived noun
Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups
For a knot K in and a regular representation of its group
into SU(2) we construct a non abelian Reidemeister torsion on the first twisted
cohomology group of the knot exterior. This non abelian Reidemeister torsion
provides a volume form on the SU(2)-representation space of . In another
way, we construct according to Casson--or more precisely taking into account
Lin's and Heusener's further works--a volume form on the SU(2)-representation
space of . Next, we compare these two apparently different points of
view--the first by means of the Reidemeister torsion and the second defined ``a
la Casson"--and finally prove that they define the same topological knot
invariant.Comment: 36 pages, 2 figures. to appear in Ann. Institut Fourie
Panel discussion: Proposals for improving OCL
During the panel session at the OCL workshop, the OCL community discussed, stimulated by short presentations by OCL experts, potential future extensions and improvements of the OCL. As such, this panel discussion continued the discussion that started at the OCL meeting in Aachen in 2013 and on which we reported in the proceedings of the last year's OCL workshop. This collaborative paper, to which each OCL expert contributed one section, summarises the panel discussion as well as describes the suggestions for further improvements in more detail.Peer ReviewedPostprint (published version
Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries
We state the intrinsic form of the Hamiltonian equations of first-order
Classical Field theories in three equivalent geometrical ways: using
multivector fields, jet fields and connections. Thus, these equations are given
in a form similar to that in which the Hamiltonian equations of mechanics are
usually given. Then, using multivector fields, we study several aspects of
these equations, such as the existence and non-uniqueness of solutions, and the
integrability problem. In particular, these problems are analyzed for the case
of Hamiltonian systems defined in a submanifold of the multimomentum bundle.
Furthermore, the existence of first integrals of these Hamiltonian equations is
considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl
general symmetries} of the system is discussed. Noether's theorem is also
stated in this context, both the ``classical'' version and its generalization
to include higher-order Cartan-Noether symmetries. Finally, the equivalence
between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be
published in J. Phys. A: Mathematical and Genera
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