3,016 research outputs found
The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories
In this paper, we investigate the main algebraic properties of the maximally
superintegrable system known as "Perlick system type I". All possible values of
the relevant parameters, and , are considered. In particular,
depending on the sign of the parameter entering in the metrics, the motion
will take place on compact or non compact Riemannian manifolds. To perform our
analysis we follow a classical variant of the so called factorization method.
Accordingly, we derive the full set of constants of motion and construct their
Poisson algebra. As it is expected for maximally superintegrable systems, the
algebraic structure will actually shed light also on the geometric features of
the trajectories, that will be depicted for different values of the initial
data and of the parameters. Especially, the crucial role played by the rational
parameter will be seen "in action".Comment: 16 pages, 7 figure
Unpacking policy processes for addressing systemic problems in technological innovation systems: the case of offshore wind in Germany
While empirical studies on technological innovation systems (TIS) usually focus on policy instruments and their suitability for curing identified weaknesses of such emerging systems, the underlying policy processes and their effects have been largely disregarded. We address this gap by exploring the style of two crucial policy-making processes and how it influences the functioning and performance of a TIS, taking the case of offshore wind in Germany. Our findings indicate important positive and negative impacts of the policy style on the TIS. For example, the muddling through character apparent in one of the policy processes negatively influenced entrepreneurial activities, knowledge development and finally technology diffusion, whereas the participatory nature of both processes had a positive impact both on TIS functioning and performance. Based on our findings we derive implications on how to improve policy making so as to foster the development of an emerging TIS
The irreducible unitary representations of the extended Poincare group in (1+1) dimensions
We prove that the extended Poincare group in (1+1) dimensions is
non-nilpotent solvable exponential, and therefore that it belongs to type I. We
determine its first and second cohomology groups in order to work out a
classification of the two-dimensional relativistic elementary systems.
Moreover, all irreducible unitary representations of the extended Poincare
group are constructed by the orbit method. The most physically interesting
class of irreducible representations corresponds to the anomaly-free
relativistic particle in (1+1) dimensions, which cannot be fully quantized.
However, we show that the corresponding coadjoint orbit of the extended
Poincare group determines a covariant maximal polynomial quantization by
unbounded operators, which is enough to ensure that the associated quantum
dynamical problem can be consistently solved, thus providing a physical
interpretation for this particular class of representations.Comment: 12 pages, Revtex 4, letter paper; Revised version of paper published
in J. Math. Phys. 45, 1156 (2004
Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
The minimal twist map introduced by B. Abdesselam, A. Chakrabarti, R.
Chakrabarti and J. Segar (Mod. Phys. Lett. A 14 (1999) 765) for the
non-standard (Jordanian) quantum sl(2,R) algebra is used to construct the twist
maps for two different non-standard quantum deformations of the (1+1)
Schrodinger algebra. Such deformations are, respectively, the symmetry algebras
of a space and a time uniform lattice discretization of the (1+1) free
Schrodinger equation. It is shown that the corresponding twist maps connect the
usual Lie symmetry approach to these discrete equations with non-standard
quantum deformations. This relationship leads to a clear interpretation of the
deformation parameter as the step of the uniform (space or time) lattice.Comment: 16 pages, LaTe
Spectrum generating algebra for the continuous spectrum of a free particle in Lobachevski space
In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum
system with purely continuous spectrum: the quantum free particle in a
Lobachevski space with constant negative curvature. The SGA contains the
geometrical symmetry algebra of the system plus a subalgebra of operators that
give the spectrum of the system and connects the eigenfunctions of the
Hamiltonian among themselves. In our case, the geometrical symmetry algebra is
and the SGA is . We start with a
representation of by functions on a realization of the
Lobachevski space given by a two sheeted hyperboloid, where the Lie algebra
commutators are the usual Poisson-Dirac brackets. Then, introduce a quantized
version of the representation in which functions are replaced by operators on a
Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the
Hamiltonian are given and "naive" ladder operators are identified. The
previously defined "naive" ladder operators shift the eigenvalues by a complex
number so that an alternative approach is necessary. This is obtained by a non
self-adjoint function of a linear combination of the ladder operators which
gives the correct relation among the eigenfunctions of the Hamiltonian. We give
an eigenfunction expansion of functions over the upper sheet of two sheeted
hyperboloid in terms of the eigenfunctions of the Hamiltonian.Comment: 23 page
Quantum mechanical spectral engineering by scaling intertwining
Using the concept of spectral engineering we explore the possibilities of
building potentials with prescribed spectra offered by a modified intertwining
technique involving operators which are the product of a standard first-order
intertwiner and a unitary scaling. In the same context we study the iterations
of such transformations finding that the scaling intertwining provides a
different and richer mechanism in designing quantum spectra with respect to
that given by the standard intertwiningComment: 8 twocolumn pages, 5 figure
Fermi-LAT Observations of High- and Intermediate-Velocity Clouds: Tracing Cosmic Rays in the Halo of the Milky Way
It is widely accepted that cosmic rays (CRs) up to at least PeV energies are
Galactic in origin. Accelerated particles are injected into the interstellar
medium where they propagate to the farthest reaches of the Milky Way, including
a surrounding halo. The composition of CRs coming to the solar system can be
measured directly and has been used to infer the details of CR propagation that
are extrapolated to the whole Galaxy. In contrast, indirect methods, such as
observations of gamma-ray emission from CR interactions with interstellar gas,
have been employed to directly probe the CR densities in distant locations
throughout the Galactic plane. In this article we use 73 months of data from
the Fermi Large Area Telescope in the energy range between 300 MeV and 10 GeV
to search for gamma-ray emission produced by CR interactions in several high-
and intermediate-velocity clouds located at up to ~ 7 kpc above the Galactic
plane. We achieve the first detection of intermediate-velocity clouds in gamma
rays and set upper limits on the emission from the remaining targets, thereby
tracing the distribution of CR nuclei in the halo for the first time. We find
that the gamma-ray emissivity per H atom decreases with increasing distance
from the plane at 97.5% confidence level. This corroborates the notion that CRs
at the relevant energies originate in the Galactic disk. The emissivity of the
upper intermediate-velocity Arch hints at a 50% decline of CR densities within
2 kpc from the plane. We compare our results to predictions of CR propagation
models.Comment: Accepted for publication in the Astrophysical Journa
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On the representation of minimal form factors in integrable quantum field theory
In this paper, we propose a new representation of the minimal form factors in integrable quantum field theories. These are solutions of the two-particle form factor equations, which have no poles on the physical sheet. Their expression constitutes the starting point for deriving higher particle form factors and, from these, the correlation functions of the theory. As such, minimal form factors are essential elements in the analysis of integrable quantum field theories. The proposed new representation arises from our recent study of form factors in-perturbed theories, where we showed that the minimal form factors decompose into elementary building blocks. Here, focusing on the paradigmatic sinh-Gordon model, we explicitly express the standard integral representation of the minimal form factor as a combination of infinitely many elementary terms, each representing the minimal form factor of a generalised perturbation of the free fermion. Our results can be readily extended to other integrable quantum field theories and open various relevant questions and discussions, from the efficiency of numerical methods in evaluating correlation functions to the foundational question of what constitutes a “reasonable” choice for the minimal form factor
Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum
The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is
revisited in the context of canonical raising and lowering operators. The
Hamiltonian is then factorized in terms of two not mutually adjoint factorizing
operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The
set of eigenvalues of this new Hamiltonian is exactly the same as the energy
spectrum of the radial oscillator and the new square-integrable eigenfunctions
are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure
New time-type and space-type non-standard quantum algebras and discrete symmetries
Starting from the classical r-matrix of the non-standard (or Jordanian)
quantum deformation of the sl(2,R) algebra, new triangular quantum deformations
for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously
constructed by using a graded contraction scheme; these are realized as
deformations of conformal algebras of (1+1)-dimensional spacetimes. Time-type
and space-type quantum algebras are considered according to the generator that
remains primitive after deformation: either the time or the space translation,
respectively. Furthermore by introducing differential-difference conformal
realizations, these families of quantum algebras are shown to be the symmetry
algebras of either a time or a space discretization of (1+1)-dimensional (wave
and Laplace) equations on uniform lattices; the relationship with the known Lie
symmetry approach to these discrete equations is established by means of twist
maps.Comment: 17 pages, LaTe
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