Spatial Localization and Relativistic Transformation of Quantum Spins

The purity of a reduced state for spins that is pure in the rest frame will most likely appear to degrade because spin and momentum become mixed when viewed by a moving observer. We show that such a boost-induced decrease in spin purity observed in a moving reference frame is intrinsically related to the spatial localization properties of the wave package observed in the rest frame. Furthermore, we prove that, for any localized pure state with separable spin and momentum in the rest frame, its reduced density matrix for spins inevitably appears to be mixed whenever viewed from a moving reference frame.Comment: 5 pages, 1 figur

Simultaneous Border-Collision and Period-Doubling Bifurcations

We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that, with sufficient non-degeneracy conditions, a locus of period-doubling bifurcations emanates non-tangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics are completely classified; in particular, we give conditions that ensure chaos.Comment: 22 pages; 5 figure

On the coexistence of position and momentum observables

We investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable

Neumark Operators and Sharp Reconstructions, the finite dimensional case

A commutative POV measure $F$ with real spectrum is characterized by the existence of a PV measure $E$ (the sharp reconstruction of $F$) with real spectrum such that $F$ can be interpreted as a randomization of $E$. This paper focuses on the relationships between this characterization of commutative POV measures and Neumark's extension theorem. In particular, we show that in the finite dimensional case there exists a relation between the Neumark operator corresponding to the extension of $F$ and the sharp reconstruction of $F$. The relevance of this result to the theory of non-ideal quantum measurement and to the definition of unsharpness is analyzed.Comment: 37 page

Suppression of Peroxisomal Enzyme Activities and Cytochrome P450 4A Isozyme Expression by Congeneric Polybrominated and Polychlorinated Biphenyls

The purpose of this study was to determine the effects of PCBs and PBBs on peroxisome proliferator-activated receptor-α-(PPARα-) associated enzyme activities or protein levels. Male Sprague-Dawley rats were administered a single IP injection (150 μ mol/kg) of either 3,3′,4,4′-tetrabromobiphenyl, 3,3′,4,4′-tetrachlorobiphenyl, 3,3′,5,5′-tetrabromobiphenyl, 2′,3,3′,4,5-pentachlorobiphenyl, 3,3′,4,4′,5-pentachlorobiphenyl, 2,2′,3,3′,5,5′-hexachlorobiphenyl, or 3,3′,4,4′,5,5′-hexabromobiphenyl in corn oil (10 ml/kg). One week later, the activities of catalase, peroxisomal fatty acyl-CoA oxidase, and peroxisomal beta-oxidation as well as cytochrome P450 4A (CYP4A) protein content were determined in subcellular liver fractions. None of the peroxisomal enzyme activities were significantly increased by any of the halogenated biphenyl congeners tested. Except for minor (approx. 25%) increases in the total CYP4A content following treatment with 2,2′,3,3′,5,5′-hexachlorobiphenyl and 3,3′,5,5′-tetrabromobiphenyl, CYP4A protein contents were not increased by any treatment. The two Ah receptor agonists, 3,3′,4,4′-tetrabromobiphenyl and 3,3′,4,4′,5-pentachlorobiphenyl, significantly diminished the liver content of CYP4A proteins and activities of the peroxisomal enzymes studied. Since a range of congeners with different biologic and toxicologic activities were selected for this study, it may be concluded that the polyhalogenated biphenyls do not induce peroxisome proliferation in the male rat, but rather certain members of this class of compounds down regulate peroxisome-associated enzymes. Since PCBs and PBBs do not increase enzyme activities and expression of proteins associated with PPARα, these agents are therefore exerting their carcinogenic and promoting activities by some other mechanism

Barycentric decomposition of quantum measurements in finite dimensions

We analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme points of the convex set are operator valued measures concentrated on a finite set of k \le d^2 points of the outcome space, d< \infty being the dimension of the Hilbert space. We prove that for second countable outcome spaces any POVM admits a Choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure. In the general case, Krein-Milman theorem is invoked to represent POVMs as barycenters of a certain set of POVMs concentrated on k \le d^2 points of the outcome space.Comment: !5 pages, no figure

Spreading of a Macroscopic Lattice Gas

We present a simple mechanical model for dynamic wetting phenomena. Metallic balls spread along a periodically corrugated surface simulating molecules of liquid advancing along a solid substrate. A vertical stack of balls mimics a liquid droplet. Stochastic motion of the balls, driven by mechanical vibration of the corrugated surface, induces diffusional motion. Simple theoretical estimates are introduced and agree with the results of the analog experiments, with numerical simulation, and with experimental data for microscopic spreading dynamics.Comment: 19 pages, LaTeX, 9 Postscript figures, to be published in Phy. Rev. E (September,1966

Master Stability Functions for Coupled Near-Identical Dynamical Systems

We derive a master stability function (MSF) for synchronization in networks of coupled dynamical systems with small but arbitrary parametric variations. Analogous to the MSF for identical systems, our generalized MSF simultaneously solves the linear stability problem for near-synchronous states (NSS) for all possible connectivity structures. We also derive a general sufficient condition for stable near-synchronization and show that the synchronization error scales linearly with the magnitude of parameter variations.Our analysis underlines significant roles played by the Laplacian eigenvectors in the study of network synchronization of near-identical systems.Comment: 11 pages, 2 figure