231 research outputs found
On the Hamiltonian structure of Ermakov systems
A canonical Hamiltonian formalism is derived for a class of Ermakov systems
specified by several different frequency functions. This class of systems
comprises all known cases of Hamiltonian Ermakov systems and can always be
reduced to quadratures. The Hamiltonian structure is explored to find exact
solutions for the Calogero system and for a noncentral potential with dynamic
symmetry. Some generalizations of these systems possessing exact solutions are
also identified and solved
A class of anisotropic (Finsler-) space-time geometries
A particular Finsler-metric proposed in [1,2] and describing a geometry with
a preferred null direction is characterized here as belonging to a subclass
contained in a larger class of Finsler-metrics with one or more preferred
directions (null, space- or timelike). The metrics are classified according to
their group of isometries. These turn out to be isomorphic to subgroups of the
Poincar\'e (Lorentz-) group complemented by the generator of a dilatation. The
arising Finsler geometries may be used for the construction of relativistic
theories testing the isotropy of space. It is shown that the Finsler space with
the only preferred null direction is the anisotropic space closest to isotropic
Minkowski-space of the full class discussed.Comment: 12 pages, latex, no figure
Performance Evaluation of Block Acquisition and Tracking Algorithms Using an Open Source GPS Receiver Platform
Location technologies have many applications in wireless communications, military and space missions, etc. US Global Positioning System (GPS) and other existing and emerging Global Navigation Satellite Systems (GNSS) are expected to provide accurate location information to enable such applications. While GNSS systems perform very well in strong signal conditions, their operation in many urban, indoor, and space applications is not robust or even impossible due to weak signals and strong distortions. The search for less costly, faster and more sensitive receivers is still in progress. As the research community addresses more and more complicated phenomena there exists a demand on flexible multimode reference receivers, associated SDKs, and development platforms which may accelerate and facilitate the research. One of such concepts is the software GPS/GNSS receiver (GPS SDR) which permits a facilitated access to algorithmic libraries and a possibility to integrate more advanced algorithms without hardware and essential software updates. The GNU-SDR and GPS-SDR open source receiver platforms are such popular examples. This paper evaluates the performance of recently proposed block-corelator techniques for acquisition and tracking of GPS signals using open source GPS-SDR platform
Quantum Lie systems and integrability conditions
The theory of Lie systems has recently been applied to Quantum Mechanics and
additionally some integrability conditions for Lie systems of differential
equations have also recently been analysed from a geometric perspective. In
this paper we use both developments to obtain a geometric theory of
integrability in Quantum Mechanics and we use it to provide a series of
non-trivial integrable quantum mechanical models and to recover some known
results from our unifying point of view
Lie systems and integrability conditions for t-dependent frequency harmonic oscillators
Time-dependent frequency harmonic oscillators (TDFHO's) are studied through
the theory of Lie systems. We show that they are related to a certain kind of
equations in the Lie group SL(2,R). Some integrability conditions appear as
conditions to be able to transform such equations into simpler ones in a very
specific way. As a particular application of our results we find t-dependent
constants of the motion for certain one-dimensional TDFHO's. Our approach
provides an unifying framework which allows us to apply our developments to all
Lie systems associated with equations in SL(2,R) and to generalise our methods
to study any Lie system
Group-invariant solutions of a nonlinear acoustics model
Based on a recent classification of subalgebras of the symmetry algebra of
the Zabolotskaya-Khokhlov equation, all similarity reductions of this equation
into ordinary differential equations are obtained. Large classes of
group-invariant solutions of the equation are also determined, and some
properties of the reduced equations and exact solutions are discussed.Comment: 14 page
Unitary Representations of the Homogeneous Lorentz Group in an O(1,1) O(2) Basis and Some Applications to Relativistic Equations
Unitary irreducible representations of the homogeneous Lorentz group O(3, 1) belonging to the principal series are reduced with respect to the subgroup O(1,1) O(2). As an application we determine the mixed basis matrix elements between O(3) and O(1,1) O(2) bases and derive recurrence relations for them. This set of functions is then used to obtain invariant expansions of solutions of the Dirac and Proca free field equations. These expansions are shown to have the correct nonrelativistic limit
On the linearization of the generalized Ermakov systems
A linearization procedure is proposed for Ermakov systems with frequency
depending on dynamic variables. The procedure applies to a wide class of
generalized Ermakov systems which are linearizable in a manner similar to that
applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into
this category but others, more generic, systems are also included
Explicit formulas for the generalized Hermite polynomials in superspace
We provide explicit formulas for the orthogonal eigenfunctions of the
supersymmetric extension of the rational Calogero-Moser-Sutherland model with
harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in
superspace. The construction relies on the triangular action of the Hamiltonian
on the supermonomial basis. This translates into determinantal expressions for
the Hamiltonian's eigenfunctions.Comment: 19 pages. This is a recasting of the second part of the first version
of hep-th/0305038 which has been splitted in two articles. In this revised
version, the introduction has been rewritten and a new appendix has been
added. To appear in JP
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