Schwinger, Pegg and Barnett and a relationship between angular and Cartesian quantum descriptions

From a development of an original idea due to Schwinger, it is shown that it is possible to recover, from the quantum description of a degree of freedom characterized by a finite number of states (\QTR{it}{i.e}., without classical counterpart) the usual canonical variables of position/momentum \QTR{it}{and} angle/angular momentum, relating, maybe surprisingly, the first as a limit of the later.Comment: 7 pages, revised version, to appear on J. Phys. A: Math and Ge

Geological Mapping of the Debussy Quadrangle (H-14) Preliminary Results

Geological mapping of Mercury is crucial to build an understanding of the history of the planet and to set the context for BepiColombo’s observations [1]. Geo-logical mapping of the Debussy quadrangle (H-14) is now underway as part of a program to map the entire planet at a scale of 1:3M using MESSENGER data [2]. The quadrangle is located in the southern hemisphere of Mercury at 0o – 90o E and 22.5o – 65o S. This will be the first high resolution map of the quadrangle as it was not imaged by Mariner 10

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

Large-uncertainty intelligent states for angular momentum and angle

The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty product. In this paper, we highlight the difference between intelligent states and minimum uncertainty states by investigating a class of intelligent states which obey the equality in the angular uncertainty relation while having an arbitrarily large uncertainty product. To develop an understanding for the uncertainties of angle and angular momentum for the large-uncertainty intelligent states we compare exact solutions with analytical approximations in two limiting cases.Comment: 20 pages, 9 figures, submitted to J. Opt. B special issue in connection with ICSSUR 2005 conferenc

On the Spectrum of Field Quadratures for a Finite Number of Photons

The spectrum and eigenstates of any field quadrature operator restricted to a finite number $N$ of photons are studied, in terms of the Hermite polynomials. By (naturally) defining \textit{approximate} eigenstates, which represent highly localized wavefunctions with up to $N$ photons, one can arrive at an appropriate notion of limit for the spectrum of the quadrature as $N$ goes to infinity, in the sense that the limit coincides with the spectrum of the infinite-dimensional quadrature operator. In particular, this notion allows the spectra of truncated phase operators to tend to the complete unit circle, as one would expect. A regular structure for the zeros of the Christoffel-Darboux kernel is also shown.Comment: 16 pages, 11 figure

Assessment of a channel catfish population in a large open river system

Estimates of dynamic rate functions for riverine channel catfish, Ictalurus punctatus (Rafinesque), populations are limited. The open nature and inherent difficulty in sampling riverine environments and the propensity for dispersal of channel catfish impede estimation of population variables. However, contemporary population models (i.e. robust design models) can incorporate the open nature of these systems. The purpose of this study was to determine channel catfish population abundance, survival and size structure and to characterize growth in the lower Platte River, Nebraska, USA. Annual survival estimates of adult channel catfish were 13%–49%, and channel catfish abundance estimates ranged from 8,281 to 24,261 fish within a 10-km sampling reach. Channel catfish were predominantly (90%

Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles

We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of identically prepared systems. We illustrate the general formalism by applying it to different scenarios of the state estimation of N independent and identically prepared two-level systems (qubits).Comment: 4 pages, RevTeX, minor modifications to the tex