3,124 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
What measurable zero point fluctuations can(not) tell us about dark energy
We show that laboratory experiments cannot measure the absolute value of dark
energy. All known experiments rely on electromagnetic interactions. They are
thus insensitive to particles and fields that interact only weakly with
ordinary matter. In addition, Josephson junction experiments only measure
differences in vacuum energy similar to Casimir force measurements. Gravity,
however, couples to the absolute value. Finally we note that Casimir force
measurements have tested zero point fluctuations up to energies of ~10 eV, well
above the dark energy scale of ~0.01 eV. Hence, the proposed cut-off in the
fluctuation spectrum is ruled out experimentally.Comment: 4 page
Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives
We consider the problem of finding commuting self-adjoint extensions of the
partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain
C_c^\infty(\Omega) where the self-adjointness is defined relative to
L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is
Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E.
Segal and B. Fuglede, and is difficult in general. In this paper, we provide a
representation-theoretic answer in the special case when \Omega=I\times\Omega_2
and I is an open interval. We then apply the results to the case when \Omega is
a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that
{e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal
basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km,
02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt,
61.44.B
The norm-1-property of a quantum observable
A normalized positive operator measure has the
norm-1-property if \no{E(X)}=1 whenever . This property reflects
the fact that the measurement outcome probabilities for the values of such
observables can be made arbitrary close to one with suitable state
preparations. Some general implications of the norm-1-property are
investigated. As case studies, localization observables, phase observables, and
phase space observables are considered.Comment: 14 page
Dihedral symmetry of periodic chain: quantization and coherent states
Our previous work on quantum kinematics and coherent states over finite
configuration spaces is extended: the configuration space is, as before, the
cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the
non-Abelian dihedral group D_n - is taken as its symmetry group. The
corresponding group related coherent states are constructed and their
overcompleteness proved. Our approach based on geometric symmetry can be used
as a kinematic framework for matrix methods in quantum chemistry of ring
molecules.Comment: 13 pages; minor changes of the tex
Zeroth Law compatibility of non-additive thermodynamics
Non-extensive thermodynamics was criticized among others by stating that the
Zeroth Law cannot be satisfied with non-additive composition rules. In this
paper we determine the general functional form of those non-additive
composition rules which are compatible with the Zeroth Law of thermodynamics.
We find that this general form is additive for the formal logarithms of the
original quantities and the familiar relations of thermodynamics apply to
these. Our result offers a possible solution to the longstanding problem about
equilibrium between extensive and non-extensive systems or systems with
different non-extensivity parameters.Comment: 18 pages, 1 figur
The Outer Envelopes of Globular Clusters. I. NGC 7089 (M2)
We present the results of a wide-field imaging survey of the periphery of the
Milky Way globular cluster NGC 7089 (M2). Data were obtained with MegaCam on
the Magellan Clay Telescope, and the Dark Energy Camera on the Blanco
Telescope. We find that M2 is embedded in a diffuse stellar envelope extending
to a radial distance of at least ( pc) -- five
times the nominal tidal radius of the cluster. The envelope appears nearly
circular in shape, has a radial density decline well described by a power law
of index , and contains approximately of the
luminosity of the entire system. While the origin of the envelope cannot be
robustly identified using the presently available data, the fact that M2 also
hosts stellar populations exhibiting a broad dispersion in the abundances of
both iron and a variety of neutron capture elements suggests that this object
might plausibly constitute the stripped nucleus of a dwarf Galaxy that was long
ago accreted and destroyed by the Milky Way.Comment: 15 pages, 12 figures, accepted for publishing in MNRA
Stellar and Planetary Properties of K2 Campaign 1 Candidates and Validation of 17 Planets, Including a Planet Receiving Earth-like Insolation
The extended Kepler mission, K2, is now providing photometry of new fields
every three months in a search for transiting planets. In a recent study,
Foreman-Mackey and collaborators presented a list of 36 planet candidates
orbiting 31 stars in K2 Campaign 1. In this contribution, we present stellar
and planetary properties for all systems. We combine ground-based
seeing-limited survey data and adaptive optics imaging with an automated
transit analysis scheme to validate 21 candidates as planets, 17 for the first
time, and identify 6 candidates as likely false positives. Of particular
interest is K2-18 (EPIC 201912552), a bright (K=8.9) M2.8 dwarf hosting a 2.23
\pm 0.25 R_Earth planet with T_eq = 272 \pm 15 K and an orbital period of 33
days. We also present two new open-source software packages which enable this
analysis. The first, isochrones, is a flexible tool for fitting theoretical
stellar models to observational data to determine stellar properties using a
nested sampling scheme to capture the multimodal nature of the posterior
distributions of the physical parameters of stars that may plausibly be
evolved. The second is vespa, a new general-purpose procedure to calculate
false positive probabilities and statistically validate transiting exoplanets.Comment: 17 pages, 5 figures, 5 tables, accepted for publication in the
Astrophysical Journal. Updated to closely reflect published version in ApJ
(2015, 809, 25
At what time does a quantum experiment have a result?
This paper provides a general method for defining a generalized quantum
observable (or POVM) that supplies properly normalized conditional
probabilities for the time of occurrence (i.e., of detection). This method
treats the time of occurrence as a probabilistic variable whose value is to be
determined by experiment and predicted by the Born rule. This avoids the
problematic assumption that a question about the time at which an event occurs
must be answered through instantaneous measurements of a projector by an
observer, common to both Rovelli (1998) and Oppenheim et al. (2000). I also
address the interpretation of experiments purporting to demonstrate the quantum
Zeno effect, used by Oppenheim et al. (2000) to justify an inherent uncertainty
for measurements of times.Comment: To appear in proceedings of 2015 ETH Zurich Workshop on Time in
Physic
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