766 research outputs found
A numerical fit of analytical to simulated density profiles in dark matter haloes
Analytical and geometrical properties of generalized power-law (GPL) density
profiles are investigated in detail. In particular, a one-to-one correspondence
is found between mathematical parameters and geometrical parameters. Then GPL
density profiles are compared with simulated dark haloes (SDH) density
profiles, and nonlinear least-absolute values and least-squares fits involving
the above mentioned five parameters (RFSM5 method) are prescribed. More
specifically, the sum of absolute values or squares of absolute logarithmic
residuals is evaluated on a large number of points making a 5-dimension
hypergrid, through a few iterations. The size is progressively reduced around a
fiducial minimum, and superpositions on nodes of earlier hypergrids are
avoided. An application is made to a sample of 17 SDHs on the scale of cluster
of galaxies, within a flat CDM cosmological model (Rasia et al. 2004).
In dealing with the mean SDH density profile, a virial radius, averaged over
the whole sample, is assigned, which allows the calculation of the remaining
parameters. Using a RFSM5 method provides a better fit with respect to other
methods. No evident correlation is found between SDH dynamical state (relaxed
or merging) and asymptotic inner slope of the logarithmic density profile or
(for SDH comparable virial masses) scaled radius. Mean values and standard
deviations of some parameters are calculated, and a comparison with previous
results is made with regard to the scaled radius. A certain degree of
degeneracy is found in fitting GPL to SDH density profiles. If it is intrinsic
to the RFSM5 method or it could be reduced by the next generation of
high-resolution simulations, still remains an open question.Comment: 44 pages, 6 figures, updated version with recent results from
high-resolution simulations (Diemand et al. 2004; Reed et al. 2005) included
in the discussion; accepted for publication on SAJ (Serbian Astronomical
Journal
Reduction Procedures in Classical and Quantum Mechanics
We present, in a pedagogical style, many instances of reduction procedures
appearing in a variety of physical situations, both classical and quantum. We
concentrate on the essential aspects of any reduction procedure, both in the
algebraic and geometrical setting, elucidating the analogies and the
differences between the classical and the quantum situations.Comment: AMS-LaTeX, 35 pages. Expanded version of the Invited review talk
delivered by G. Marmo at XXIst International Workshop On Differential
Geometric Methods In Theoretical Mechanics, Madrid (Spain), 2006. To appear
in Int. J. Geom. Methods in Modern Physic
Wigner-Weyl isomorphism for quantum mechanics on Lie groups
The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie
group is developed in detail. Several New features are shown to arise which
have no counterparts in the familiar Cartesian case. Notable among these is the
notion of a `semiquantised phase space', a structure on which the Weyl symbols
of operators turn out to be naturally defined and, figuratively speaking,
located midway between the classical phase space and the Hilbert space
of square integrable functions on . General expressions for the star product
for Weyl symbols are presented and explicitly worked out for the angle-angular
momentum case.Comment: 32 pages, Latex2
Localization in the Rindler Wedge
One of the striking features of QED is that charged particles create a
coherent cloud of photons. The resultant coherent state vectors of photons
generate a non-trivial representation of the localized algebra of observables
that do not support a representation of the Lorentz group: Lorentz symmetry is
spontaneously broken. We show in particular that Lorentz boost generators
diverge in this representation, a result shown also in [1] (See also [2]).
Localization of observables, for example in the Rindler wedge, uses Poincar\'e
invariance in an essential way [3]. Hence in the presence of charged fields,
the photon observables cannot be localized in the Rindler wedge.
These observations may have a bearing on the black hole information loss
paradox, as the physics in the exterior of the black hole has points of
resemblance to that in the Rindler wedge.Comment: 11 page
Dark matter haloes: an additional criterion for the choice of fitting density profiles
Simulated dark matter haloes are fitted by self-similar, universal density
profiles, where the scaled parameters depend only on a scaled (truncation)
radius which, in turn, is supposed to be independent on the mass and the
formation redshift. A criterion for the choice of the best fitting density
profile is proposed, with regard to a set of high-resolution simulations, where
some averaging procedure on scaled density profiles has been performed, in
connection with a number of fitting density profiles. An application is made to
a pair of sets each made of a dozen of high-resolution simulations, which are
available in literature, in connection with two currently used fitting density
profiles, where the dependence of the scaled radius on the mass and the
formation redshift, may be neglected to a first extent. Some features of the
early evolution of dark matter haloes represented by fitting density profiles,
are discussed in the limit of the spherical top-hat model.Comment: 62 pages, 9 figures, accepted for publication on SAJ (Serbian
Astronomical Journal), paragraph and reference added for section
Wigner distributions for finite dimensional quantum systems: An algebraic approach
We discuss questions pertaining to the definition of `momentum', `momentum
space', `phase space', and `Wigner distributions'; for finite dimensional
quantum systems. For such systems, where traditional concepts of `momenta'
established for continuum situations offer little help, we propose a physically
reasonable and mathematically tangible definition and use it for the purpose of
setting up Wigner distributions in a purely algebraic manner. It is found that
the point of view adopted here is limited to odd dimensional systems only. The
mathematical reasons which force this situation are examined in detail.Comment: Latex, 13 page
Phase-space descriptions of operators and the Wigner distribution in quantum mechanics II. The finite dimensional case
A complete solution to the problem of setting up Wigner distribution for
N-level quantum systems is presented. The scheme makes use of some of the ideas
introduced by Dirac in the course of defining functions of noncommuting
observables and works uniformly for all N. Further, the construction developed
here has the virtue of being essentially input-free in that it merely requires
finding a square root of a certain N^2 x N^2 complex symmetric matrix, a task
which, as is shown, can always be accomplished analytically. As an
illustration, the case of a single qubit is considered in some detail and it is
shown that one recovers the result of Feynman and Wootters for this case
without recourse to any auxiliary constructs.Comment: 14 pages, typos corrected, para and references added in introduction,
submitted to Jour. Phys.
The Schwinger Representation of a Group: Concept and Applications
The concept of the Schwinger Representation of a finite or compact simple Lie
group is set up as a multiplicity-free direct sum of all the unitary
irreducible representations of the group. This is abstracted from the
properties of the Schwinger oscillator construction for SU(2), and its
relevance in several quantum mechanical contexts is highlighted. The Schwinger
representations for and SU(n) for all are constructed via
specific carrier spaces and group actions. In the SU(2) case connections to the
oscillator construction and to Majorana's theorem on pure states for any spin
are worked out. The role of the Schwinger Representation in setting up the
Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is
brought out.Comment: Latex, 17 page
Non-symplectic symmetries and bi-Hamiltonian structures of the rational Harmonic Oscillator
The existence of bi-Hamiltonian structures for the rational Harmonic
Oscillator (non-central harmonic oscillator with rational ratio of frequencies)
is analyzed by making use of the geometric theory of symmetries. We prove that
these additional structures are a consequence of the existence of dynamical
symmetries of non-symplectic (non-canonical) type. The associated recursion
operators are also obtained.Comment: 10 pages, submitted to J. Phys. A:Math. Ge
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