4,755 research outputs found
Iterated function systems, representations, and Hilbert space
This paper studies a general class of Iterated Function Systems (IFS). No
contractivity assumptions are made, other than the existence of some compact
attractor. The possibility of escape to infinity is considered. Our present
approach is based on Hilbert space, and the theory of representations of the
Cuntz algebras O_n, n=2,3,.... While the more traditional approaches to IFS's
start with some equilibrium measure, ours doesn't. Rather, we construct a
Hilbert space directly from a given IFS; and our construction uses instead
families of measures. Starting with a fixed IFS S_n, with n branches, we prove
existence of an associated representation of O_n, and we show that the
representation is universal in a certain sense. We further prove a theorem
about a direct correspondence between a given system S_n, and an associated
sub-representation of the universal representation of O_n.Comment: 22 pages, 3 figures containing 7 EPS graphics; LaTeX2e ("elsart"
document class); v2 reflects change in Comments onl
Wavelets in mathematical physics: q-oscillators
We construct representations of a q-oscillator algebra by operators on Fock
space on positive matrices. They emerge from a multiresolution scaling
construction used in wavelet analysis. The representations of the Cuntz Algebra
arising from this multiresolution analysis are contained as a special case in
the Fock Space construction.Comment: (03/11/03):18 pages; LaTeX2e, "article" document class with
"letterpaper" option An outline was added under the abstract (p.1),
paragraphs added to Introduction (p.2), mat'l added to Proofs in Theorems 1
and 6 (pgs.5&17), material added to text for the conclusion (p.17), one add'l
reference added [12]. (04/22/03):"number 1" replace with "term C" (p.9),
single sentences reformed into a one paragraph (p.13), QED symbol moved up
one paragraph and last paragraph labeled as "Concluding Remarks.
The Measure of a Measurement
While finite non-commutative operator systems lie at the foundation of
quantum measurement, they are also tools for understanding geometric iterations
as used in the theory of iterated function systems (IFSs) and in wavelet
analysis. Key is a certain splitting of the total Hilbert space and its
recursive iterations to further iterated subdivisions. This paper explores some
implications for associated probability measures (in the classical sense of
measure theory), specifically their fractal components.
We identify a fractal scale in a family of Borel probability measures
on the unit interval which arises independently in quantum information
theory and in wavelet analysis. The scales we find satisfy and , some . We identify these
scales by considering the asymptotic properties of
where are dyadic subintervals, and .Comment: 18 pages, 3 figures, and reference
Ages, metallicities and -element enhancement for galaxies in Hickson compact groups
Central velocity dispersions and eight line-strength Lick indices have been
determined from 1.3 resolution long-slit spectra of 16 elliptical
galaxies in Hickson compact groups. These data were used to determine galaxy
properties (ages, metallicities and -element enhancements) and allowed
a comparison with the parameters determined for a sample of galaxies in lower
density environments, studied by Gonz\'alez (1993). The stellar population
parameters were derived by comparison to single stellar population models of
Thomas et al. (2003) and to a new set of SSP models for the indices Mg,
Fe5270 and Fe5335 based on synthetic spetra. These models, based on an update
version of the fitting functions presented in Barbuy et al. (2003), are fully
described here. Our main results are: (1) the two samples have similar mean
values for the metallicities and [/Fe] ratios, (2) the majority of the
galaxies in compact groups seem to be old (median age of 14 Gyr for eight
galaxies for which ages could be derived), in agreement with recent work by
Proctor et al. (2004). These findings support two possible scenarios: compact
groups are either young systems whose members have recently assembled and had
not enough time to experience any merging yet or, instead, they are old systems
that have avoided merging since their time of formation.Comment: Accepted for publication in A
Spatially resolved spectroscopy of Coma cluster early-type galaxies IV. Completing the dataset
The long-slit spectra obtained along the minor axis, offset major axis and
diagonal axis are presented for 12 E and S0 galaxies of the Coma cluster drawn
from a magnitude-limited sample studied before. The rotation curves, velocity
dispersion profiles and the H_3 and H_4 coefficients of the Hermite
decomposition of the line of sight velocity distribution are derived. The
radial profiles of the Hbeta, Mg, and Fe line strength indices are measured
too. In addition, the surface photometry of the central regions of a subsample
of 4 galaxies recently obtained with Hubble Space Telescope is presented. The
data will be used to construct dynamical models of the galaxies and study their
stellar populations.Comment: 40 pages, 7 figures, 6 tables. Accepted for publication in ApJ
The existence problem for dynamics of dissipative systems in quantum probability
Motivated by existence problems for dissipative systems arising naturally in
lattice models from quantum statistical mechanics, we consider the following
-algebraic setting: A given hermitian dissipative mapping is
densely defined in a unital -algebra . The identity
element in is also in the domain of . Completely
dissipative maps are defined by the requirement that the induced maps,
, are dissipative on the by complex
matrices over for all . We establish the existence of different
types of maximal extensions of completely dissipative maps. If the enveloping
von Neumann algebra of is injective, we show the existence of an
extension of which is the infinitesimal generator of a quantum
dynamical semigroup of completely positive maps in the von Neumann algebra. If
is a given well-behaved *-derivation, then we show that each of the
maps and is completely dissipative.Comment: 24 pages, LaTeX/REVTeX v. 4.0, submitted to J. Math. Phys.; PACS 02.,
02.10.Hh, 02.30.Tb, 03.65.-w, 05.30.-
Stellar kinematics for the central spheroid in the Polar Disk Galaxy NGC4650A
We have obtained high angular resolution, high signal-to-noise spectra of the
Calcium triplet absorption lines on the photometric axes of the stellar
spheroid in the polar disk galaxy NGC4650A. Along the major axis, the observed
rotation and velocity dispersion measurements show the presence of a
kinematically decoupled nucleus, and a flat velocity dispersion profile. The
minor axis kinematics is determined for the first time: along this direction
some rotation is measured, and the velocity dispersion is nearly constant and
slightly increases at larger distances from the center. The new high resolution
kinematic data suggest that the stellar component in NGC4650A resembles a
nearly-exponential oblate spheroid supported by rotation. The main implications
of these results on the previous mass models for NGC4650A are discussed.
Moreover, the new kinematic data set constraints on current models for the
formation scenarios of Polar Ring Galaxies (PRGs), supporting a slow accretion
rather then a secondary strong dissipative event.Comment: 25 pages, 8 figures, accepted for publication in the Astrophysical
Journa
Generalization of Classical Statistical Mechanics to Quantum Mechanics and Stable Property of Condensed Matter
Classical statistical average values are generally generalized to average
values of quantum mechanics, it is discovered that quantum mechanics is direct
generalization of classical statistical mechanics, and we generally deduce both
a new general continuous eigenvalue equation and a general discrete eigenvalue
equation in quantum mechanics, and discover that a eigenvalue of quantum
mechanics is just an extreme value of an operator in possibility distribution,
the eigenvalue f is just classical observable quantity. A general classical
statistical uncertain relation is further given, the general classical
statistical uncertain relation is generally generalized to quantum uncertainty
principle, the two lost conditions in classical uncertain relation and quantum
uncertainty principle, respectively, are found. We generally expound the
relations among uncertainty principle, singularity and condensed matter
stability, discover that quantum uncertainty principle prevents from the
appearance of singularity of the electromagnetic potential between nucleus and
electrons, and give the failure conditions of quantum uncertainty principle.
Finally, we discover that the classical limit of quantum mechanics is classical
statistical mechanics, the classical statistical mechanics may further be
degenerated to classical mechanics, and we discover that only saying that the
classical limit of quantum mechanics is classical mechanics is mistake. As
application examples, we deduce both Shrodinger equation and state
superposition principle, deduce that there exist decoherent factor from a
general mathematical representation of state superposition principle, and the
consistent difficulty between statistical interpretation of quantum mechanics
and determinant property of classical mechanics is overcome.Comment: 10 page
Magnetic and electronic structures of superconducting RuSrGdCuO
The coexistence of ferromagnetism and superconductivity in
RuSrGdCuO was reported both from experiments (by Tallon et. al.)
and first-principles calculations (by Pickett et. al.). Here we report that our
first-principles full-potential linearized augmented plane wave (FLAPW)
calculations, employing the precise crystal structure with structural
distortions (i.e., RuO rotations) determined by neutron diffraction,
demonstrate that antiferromagnetic ordering of the Ru moments is energetically
favored over the previously proposed ferromagnetic ordering. Our results are
consistent with recently performed magnetic neutron diffraction experiments
(Lynn et. al). Ru states, which are responsible for the magnetism,
have only a very small interaction with Cu states, which results in a
small exchange splitting of these states. The Fermi surface, characterized by
strongly hybridized orbitals, has nesting features similar to those
in the two-dimensional high cuprate superconductors.Comment: 6 pages,6 figures, accepted for publication in Phys. Rev.
Superconductivity in the Cuprates as a Consequence of Antiferromagnetism and a Large Hole Density of States
We briefly review a theory for the cuprates that has been recently proposed
based on the movement and interaction of holes in antiferromagnetic (AF)
backgrounds. A robust peak in the hole density of states (DOS) is crucial to
produce a large critical temperature once a source of hole attraction is
identified. The predictions of this scenario are compared with experiments. The
stability of the calculations after modifying some of the original assumptions
is addressed. We find that if the dispersion is changed from an
antiferromagnetic band at half-filling to a tight binding
narrow band at , the main conclusions of the approach remain
basically the same i.e. superconductivity appears in the -channel and is enhanced by a large DOS. The main features
distinguishing these ideas from more standard theories based on
antiferromagnetic correlations are here discussed.Comment: RevTex, 7 pages, 5 figures are available on reques
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