Bound states of PT-symmetric separable potentials

All of the PT-symmetric potentials that have been studied so far have been local. In this paper nonlocal PT-symmetric separable potentials of the form $V(x,y)=i\epsilon[U(x)U(y)-U(-x)U(-y)]$, where $U(x)$ is real, are examined. Two specific models are examined. In each case it is shown that there is a parametric region of the coupling strength $\epsilon$ for which the PT symmetry of the Hamiltonian is unbroken and the bound-state energies are real. The critical values of $\epsilon$ that bound this region are calculated.Comment: 10 pages, 3 figure

Household wealth and adolescents' social-emotional functioning in schools.

This study attempts a two-part shift in educational research narrowly fixated on the socioeconomic determinants of student test-score performance. First, we focus on variations in how to measure wealth. Second, we move beyond achievement and focus on the wealth determinants of adolescents' social-emotional competencies. Using data from a nationally-representative sample of US eighth graders, we find that the correlation between wealth and social-emotional competencies varies according to how the partitions among the upper class, the middle and working classes, and the poor are defined. By emphasizing wealth in the production of classed social-emotional competencies not captured by test scores, our findings suggest that the growth of household wealth has a more salient effect for lower- and middle-class adolescents than the highest class which appears to have the least to gain, in terms of social-emotional competencies, from an increase in household wealth

The Population Dynamics and Distribution of Corbicula Manilensis (Philippi) in a Spring-fed Central Florida Stream

Asiatic clams (Corbicula manilensis Philippi) were sampled at twelve stations randomly located along a 16-km stretch of the Wekiva River, Florida, every three months fro August 1976 to June 1977. Clams were found at most stations. Their abundance ranged from 4 to 1210 per m2. Mean numbers of Corbicula were highest at stations where the bottom sediments were primarily sand and lowest at stations where the bottom sediments were silt and decomposing organic matter. A linear relationship between water temperature, water depth, current velocity, total alkalinity, and pH, and the abundance and distribution of Corbicula was not evident. Seasonally, the abundance of Corbicula was highest in August 1976 and lowest in December 1976. The small size of the specimens suggest a recent invasion of Corbicula into the Wekiva River. The mean shell length of Corbicula in the river was 13.5 mm. The shell lengths of the largest clams ranged from 25.3 mm to 27.2 mm. Large clams were collected in December 1976 (mean shell length = 13.7 mm), whereas small clams were collected in March 1977 (mean shell length = 13.1 mm). Shell width and shell length were linearly correlated (r - 9.98 to 0.99), as were shell breadth and shell length (r = 0.96 to 0.99). The correlation between shell length and the number of rings on the shell was lower (r = 0.68 to 0.88). Clams with smaller rings (more rings per unit length) were found at downstream stations, where abundance was hing, whereas clams with larger rings (fewer rings per unit length) were found at upstream stations, where abundance was low. The data suggest that relationships between age and size depend on the habitat in which the organisms live

Fossil Spores of the Alleghenian Coals in Indiana

Indiana Geological Survey Report of Progress 4In this report the significance of spores in plant life cycles is discussed briefly. The term “miospore” is proposed for fossil spores and spore-like bodies under 200 micra in size. Sampling and coal preparation are outlined, the stratigraphy of the Alleghenian series in Indiana is sketched in broad strokes, and the underlying principles of the theory of coal correlation are discussed. Percentage relationships of miospore genera have been established for the nine known coal seams of the Alleghenian series in Indiana, and some unknown coal beds have been identified on the basis of the relative abundance of certain genera.Indiana Department of Conservatio

Miospore Analysis of the Pottsville Coals of Indiana

Indiana Geological Survey Bulletin 13Ninety-eight samples were collected for this study at 85 localities in 12 Indiana Counties. Percentage relationships of miospore genera and relative abundances of species were determined for these samples and can be used successfully in correlating coal beds within the Pottsville series (Pennsylvanian System). Two formations, the Mansfield and the Brazil, constitute the Pottsville Series in Indiana. Miospore analysis revealed seven distinct spore assemblages for samples of coals from the Mansfield Formation and indicates the need for further detailed study of these coals. Samples from the Brazil Formation displayed eight distinct assemblages. These spore patterns are useful for dividing the Brazil Formation into eight zones and indicate that the formation may have more coal seams than geologists have previously thought.Indiana Department of Conservatio

A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. III : Measurements and von Neumann Projection/Collapse Rule

Supmech, the universal mechanics developed in the previous two papers, accommodates both quantum and classical mechanics as subdisciplines (a brief outline is included for completeness); this feature facilitates, in a supmech based treatment of quantum measurements, an unambiguous treatment of the apparatus as a quantum system approximated well by a classical one. Taking explicitly into consideration the fact that observations on the apparatus are made when it has `settled down after the measurement interaction' and are restricted to macroscopically distinguishable pointer readings, the unwanted superpositions of (system + apparatus) states are shown to be suppressed; this provides a genuinely physics based justification for the (traditionally \emph{postulated}) von Neumann projection/collapse rule. The decoherence mechanism brought into play by the stated observational constraints is free from the objections against the traditional decoherence program.Comment: 29 pages; one section and two references added; results unchange

Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits

A complete orthonormal basis of N-qutrit unitary operators drawn from the Pauli Group consists of the identity and 9^N-1 traceless operators. The traceless ones partition into 3^N+1 maximally commuting subsets (MCS's) of 3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3^N are isomorphic to all MCS's, and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS's. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators partition into 28 MCS's with less rigid structure allowing for the coexistence of separable, partially-entangled, and totally entangled (GHZ-like) bases. However, a minimum of 16 GHZ-like bases must occur. Every basis state is described by an N-digit trinary number consisting of the eigenvalues of N observables constructed from the corresponding MCS.Comment: LaTeX, 10 pages, 2 references adde

Complex trajectory method in time-dependent WKB

We present a significant improvement to a time-dependent WKB (TDWKB) formulation developed by Boiron and Lombardi [JCP {\bf108}, 3431 (1998)] in which the TDWKB equations are solved along classical trajectories that propagate in the complex plane. Boiron and Lombardi showed that the method gives very good agreement with the exact quantum mechanical result as long as the wavefunction does not exhibit interference effects such as oscillations and nodes. In this paper we show that this limitation can be overcome by superposing the contributions of crossing trajectories. We also demonstrate that the approximation improves when incorporating higher order terms in the expansion. These improvements could make the TDWKB formulation a competitive alternative to current time-dependent semiclassical methods

The Fermionic Density-functional at Feshbach Resonance

We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature.The atoms interact via a short range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second order perturbation theory, has the same density dependence as the first order exchange energy, and the two almost exactly cancel each other at Feshbach resonance irrespective of the shape of the potential, provided $(\mu r_s) >> 1$. Here $(\mu)^{-1}$ is the range of the two-body potential, and $r_s$ is defined through the number density $n=3/(4\pi r_s^3)$. The implications of this result for universality is discussed.Comment: Five pages, one table. accepted for publication in PR

Resonator/zero-Qubit architecture for superconducting qubits

We analyze the performance of the Resonator/zero-Qubit (RezQu) architecture in which the qubits are complemented with memory resonators and coupled via a resonator bus. Separating the stored information from the rest of the processing circuit by at least two coupling steps and the zero qubit state results in a significant increase of the ON/OFF ratio and the reduction of the idling error. Assuming no decoherence, we calculate such idling error, as well as the errors for the MOVE operation and tunneling measurement, and show that the RezQu architecture can provide high fidelity performance required for medium-scale quantum information processing.Comment: 11 pages, 5 figure