Volume of the quantum mechanical state space

The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of the determinant in the general setting too. The case when the state space is endowed with a monotone metric or a pull-back metric is considered too, we give formulas to compute the volume of the state space with respect to the given Riemannian metric. We present the volume of the space of qubits with respect to various monotone metrics. It turns out that the volume of the space of qubits can be infinite too. We characterize those monotone metrics which generates infinite volume.Comment: 17 page

Apollo 9 multiband photography experiment 5065 Interim post-flight calibration report

Camera and filter postflight spectrum analysis for Apollo 9 multiband photography experimen

High-Temperature Expansions of Bures and Fisher Information Priors

For certain infinite and finite-dimensional thermal systems, we obtain --- incorporating quantum-theoretic considerations into Bayesian thermostatistical investigations of Lavenda --- high-temperature expansions of priors over inverse temperature beta induced by volume elements ("quantum Jeffreys' priors) of Bures metrics. Similarly to Lavenda's results based on volume elements (Jeffreys' priors) of (classical) Fisher information metrics, we find that in the limit beta -> 0, the quantum-theoretic priors either conform to Jeffreys' rule for variables over [0,infinity], by being proportional to 1/beta, or to the Bayes-Laplace principle of insufficient reason, by being constant. Whether a system adheres to one rule or to the other appears to depend upon its number of degrees of freedom.Comment: Six pages, LaTeX. The title has been shortened (and then further modified), at the suggestion of a colleague. Other minor change

Traveling sealer for contoured table Patent

Sealing apparatus for joining two pieces of frangible material

Bures distance between two displaced thermal states

The Bures distance between two displaced thermal states and the corresponding geometric quantities (statistical metric, volume element, scalar curvature) are computed. Under nonunitary (dissipative) dynamics, the statistical distance shows the same general features previously reported in the literature by Braunstein and Milburn for two--state systems. The scalar curvature turns out to have new interesting properties when compared to the curvature associated with squeezed thermal states.Comment: 3 pages, RevTeX, no figure

On the structure of the body of states with positive partial transpose

We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random boundary state to be separable, provided the random states are generated uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An analogous property holds for the set of positive-partial-transpose states for an arbitrary bipartite system.Comment: 10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma

Quantum and Fisher Information from the Husimi and Related Distributions

The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262 [1996]). In the former work, a metric (the Monge one, specifically) over generalized Husimi distributions was employed to define a distance between two arbitrary density matrices. In the Petz-Sudar work (completing a program of Chentsov), the quantum analogue of the (classically unique) Fisher information (montone) metric of a probability simplex was extended to define an uncountable infinitude of Riemannian (also monotone) metrics on the set of positive definite density matrices. We pose here the questions of what is the specific/unique Fisher information metric for the (classically-defined) Husimi distributions and how does it relate to the infinitude of (quantum) metrics over the density matrices of Petz and Sudar? We find a highly proximate (small relative entropy) relationship between the probability distribution (the quantum Jeffreys' prior) that yields quantum universal data compression, and that which (following Clarke and Barron) gives its classical counterpart. We also investigate the Fisher information metrics corresponding to the escort Husimi, positive-P and certain Gaussian probability distributions, as well as, in some sense, the discrete Wigner pseudoprobability. The comparative noninformativity of prior probability distributions -- recently studied by Srednicki (Phys. Rev. A 71, 052107 [2005]) -- formed by normalizing the volume elements of the various information metrics, is also discussed in our context.Comment: 27 pages, 10 figures, slight revisions, to appear in J. Math. Phy

Spin-dependent transport in molecular tunnel junctions

We present measurements of magnetic tunnel junctions made using a self-assembled-monolayer molecular barrier. Ni/octanethiol/Ni samples were fabricated in a nanopore geometry. The devices exhibit significant changes in resistance as the angle between the magnetic moments in the two electrodes is varied, demonstrating that low-energy electrons can traverse the molecular barrier while maintaining spin coherence. An analysis of the voltage and temperature dependence of the data suggests that the spin-coherent transport signals can be degraded by localized states in the molecular barriers.Comment: 4 pages, 5 color figure

Molecular Gas, Dust and Star Formation in Galaxies: II. Dust properties and scalings in \sim\ 1600 nearby galaxies

We aim to characterize the relationship between dust properties. We also aim to provide equations to estimate accurate dust properties from limited observational datasets. We assemble a sample of 1,630 nearby (z<0.1) galaxies-over a large range of Mstar, SFR - with multi-wavelength observations available from wise, iras, planck and/or SCUBA. The characterization of dust emission comes from SED fitting using Draine & Li dust models, which we parametrize using two components (warm and cold ). The subsample of these galaxies with global measurements of CO and/or HI are used to explore the molecular and/or atomic gas content of the galaxies. The total Lir, Mdust and dust temperature of the cold component (Tc) form a plane that we refer to as the dust plane. A galaxy's sSFR drives its position on the dust plane: starburst galaxies show higher Lir, Mdust and Tc compared to Main Sequence and passive galaxies. Starburst galaxies also show higher specific Mdust (Mdust/Mstar) and specific Mgas (Mgas/Mstar). The Mdust is more closely correlated with the total Mgas (atomic plus molecular) than with the individual components. Our multi wavelength data allows us to define several equations to estimate Lir, Mdust and Tc from one or two monochromatic luminosities in the infrared and/or sub-millimeter. We estimate the dust mass and infrared luminosity from a single monochromatic luminosity within the R-J tail of the dust emission, with errors of 0.12 and 0.20dex, respectively. These errors are reduced to 0.05 and 0.10 dex, respectively, if the Tc is used. The Mdust is correlated with the total Mism (Mism \propto Mdust^0.7). For galaxies with Mstar 8.5<log(Mstar/Msun) < 11.9, the conversion factor \alpha_850mum shows a large scatter (rms=0.29dex). The SF mode of a galaxy shows a correlation with both the Mgass and Mdust: high Mdust/Mstar galaxies are gas-rich and show the highest SFRs.Comment: 24 pages, 28 figures, 6 tables, Accepted for publication in A&

On Metric Dimension of Functigraphs

The \emph{metric dimension} of a graph $G$, denoted by $\dim(G)$, is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let $G_1$ and $G_2$ be disjoint copies of a graph $G$ and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid v=f(u)\}$. We study how metric dimension behaves in passing from $G$ to $C(G,f)$ by first showing that $2 \le \dim(C(G, f)) \le 2n-3$, if $G$ is a connected graph of order $n \ge 3$ and $f$ is any function. We further investigate the metric dimension of functigraphs on complete graphs and on cycles.Comment: 10 pages, 7 figure