Observation of Three-dimensional Long-range Order in Smaller Ion Coulomb Crystals in an rf Trap

Three-dimensional long-range ordered structures in smaller and near-spherically symmetric Coulomb crystals of ^{40}Ca^+ ions confined in a linear rf Paul trap have been observed when the number of ions exceeds ~1000 ions. This result is unexpected from ground state molecular dynamics (MD) simulations, but found to be in agreement with MD simulations of metastable ion configurations. Previously, three-dimensional long-range ordered structures have only been reported in Penning traps in systems of ~50,000 ions or more.Comment: 5 pages; 4 figures; to appear in Phys. Rev. Lett.; changed content

Spectral Conditions on the State of a Composite Quantum System Implying its Separability

For any unitarily invariant convex function F on the states of a composite quantum system which isolates the trace there is a critical constant C such that F(w)<= C for a state w implies that w is not entangled; and for any possible D > C there are entangled states v with F(v)=D. Upper- and lower bounds on C are given. The critical values of some F's for qubit/qubit and qubit/qutrit bipartite systems are computed. Simple conditions on the spectrum of a state guaranteeing separability are obtained. It is shown that the thermal equilbrium states specified by any Hamiltonian of an arbitrary compositum are separable if the temperature is high enough.Comment: Corrects 1. of Lemma 2, and the (under)statement of Proposition 7 of the earlier version

A statistical investigation of the effects contributed by tape recorders and by wow and flutter of magnetic tape on the accuracy of a telemetry system Technical report no. 15

Effects contributed by tape recorders and by wow and flutter of magnetic tape on accuracy of telemetry syste

Philip Morris Corporate Headquarters Building

The temporary support of three city streets, a subway tunnel, and a high-rise office tower during the construction of the Philip Morris Corporate Headquarters Building is discussed. The results of an extensive field exploration program, consisting of test borings, probes, and geologic mapping were evaluated for the design of temporary support systems; i.e., rock anchors and rakers. Borehole extensometers and conventional optical survey techniques were successfully used to monitor movements of the adjacent structures during demolition operations of a building that occupied the site. Minimal movements were measured during demolition. At the northeast corner of the site, six heavily loaded columns were scheduled to bear in mica schist rock above an active subway tunne. Based on an extensive geologic mapping program and a complex series of borings, the rock foliation was founded to be favorably oriented, allowing the footings to be founded in rock above the subway tunnel

Two-Qubit Separability Probabilities and Beta Functions

Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and quant-ph/0304041), exact formulas are available (both in terms of the Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and (n(n-1)/2-1)-dimensional volumes of the complex and real n x n density matrices. However, no comparable formulas are available for the volumes (and, hence, probabilities) of various separable subsets of them. We seek to clarify this situation for the Hilbert-Schmidt metric for the simplest possible case of n=4, that is, the two-qubit systems. Making use of the density matrix (rho) parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce each of the real and complex volume problems to the calculation of a one-dimensional integral, the single relevant variable being a certain ratio of diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated integrand in each case is the product of a known (highly oscillatory near nu=1) jacobian and a certain unknown univariate function, which our extensive numerical (quasi-Monte Carlo) computations indicate is very closely proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2, b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case. Assuming the full applicability of these specific incomplete beta functions, we undertake separable volume calculations.Comment: 17 pages, 4 figures, paper is substantially rewritten and reorganized, with the quasi-Monte Carlo integration sample size being greatly increase