The Bargmann representation for the quantum mechanics on a sphere

The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in: K. Kowalski and J. Rembielinski, J. Phys. A: Math. Gen. 33, 6035 (2000). The connection is discussed between the introduced formalism and the standard approach based on the Hilbert space of square integrable functions on a sphere S^2.Comment: LaTe

Coherent states on spheres

We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated phase space T*(S^d). These coherent states are NOT of Perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators. We describe as well the Segal-Bargmann representation for the system, the associated unitary Segal-Bargmann transform, and a natural inversion formula. Although many of these results are in principle special cases of the results of B. Hall and M. Stenzel, we give here a substantially different description based on ideas of T. Thiemann and of K. Kowalski and J. Rembielinski. All of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space. We focus on the sphere case in order to be able to carry out the calculations in a self-contained and explicit way.Comment: Revised version. Submitted to J. Mathematical Physic

On the uncertainty relations and squeezed states for the quantum mechanics on a circle

The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in the context of the uncertainty relations.Comment: 4 figure

Aerodynamics of lift fan V/STOL aircraft

Aerodynamic characteristics of lift fan installation for direct lift V/STOL aircraf

Object orientation without extending Z

The good news of this paper is that without extending Z, we can elegantly specify object-oriented systems, including encapsulation, inheritance and subtype polymorphism (dynamic dispatch). The bad news is that this specification style is rather different to normal Z specifications, more abstract and axiomatic, which means that it is not so well supported by current Z tools such as animators. It also enforces behavioural subtyping, unlike most object-oriented programming languages. This paper explains the proposed style, with examples, and discusses its advantages and disadvantages

Signatures of four-particle correlations associated with exciton-carrier interactions in coherent spectroscopy on bulk GaAs

Transient four-wave mixing studies of bulk GaAs under conditions of broad bandwidth excitation of primarily interband transitions have enabled four-particle correlations tied to degenerate (exciton-exciton) and nondegenerate (exciton-carrier) interactions to be studied. Real two-dimensional Fourier-transform spectroscopy (2DFTS) spectra reveal a complex response at the heavy-hole exciton emission energy that varies with the absorption energy, ranging from dispersive on the diagonal, through absorptive for low-energy interband transitions to dispersive with the opposite sign for interband transitions high above band gap. Simulations using a multilevel model augmented by many-body effects provide excellent agreement with the 2DFTS experiments and indicate that excitation-induced dephasing (EID) and excitation-induced shift (EIS) affect degenerate and nondegenerate interactions equivalently, with stronger exciton-carrier coupling relative to exciton-exciton coupling by approximately an order of magnitude. These simulations also indicate that EID effects are three times stronger than EIS in contributing to the coherent response of the semiconductor

Snow water equivalent determination by microwave radiometry

One of the most important parameters for accurate snowmelt runoff prediction is snow water equivalent (SWE) which is contentionally monitored using observations made at widely scattered points in or around specific watersheds. Remote sensors which provide data with better spatial and temporal coverage can be used to improve the SWE estimates. Microwave radiation, which can penetrate through a snowpack, may be used to infer the SWE. Calculations made from a microscopic scattering model were used to simulate the effect of varying SWE on the microwave brightness temperature. Data obtained from truck mounted, airborne and spaceborne systems from various test sites were studied. The simulated SWE compares favorable with the measured SWE. In addition, whether the underlying soil is frozen or thawed can be discriminated successfully on the basis of the polarization of the microwave radiation

Differentiation and growth of kype skeletal tissues in anadromous male Atlantic salmon (Salmo salar)

The re-initiation of bone development in adult starving Atlantic salmon (Salmo salar) during their energetically expensive upstream migration is remarkable and deserves closer examination. Dramatic alterations of the skull bones and teeth, most prominently, the development of a kype in males, are widely known but little studied or understood. We describe the microstructure and the cellular processes involved in the formation of the skeletal tissues of the kype. Fresh bone material, obtained from animals migrating upstream was subjected to radiological, histological or histochemical analysis. We show that the kype is, in part, composed of rapidly growing skeletal needles arising at the tip of the dentary. Proximally, the needles anastomose into a spongiosa-like meshwork which retains connective tissue inside bone marrow spaces. Ventrally, the needles blend into Sharpey fiber bone. Skeletal needles and Sharpey fiber bone can be distinguished from the compact bone of the dentary by radiography. Rapid formation of the skeleton of the kype is demonstrated by the presence of numerous osteoblasts, a broad distal osteoid zone, and the appearance of proteoglycans at the growth zone. The mode of bone formation in anadromous males can be described as 'making bone as fast as possible and with as little material as possible'. Unlike the normal compact bone of the dentary, the new skeletal tissue contains chondrocytes and cartilaginous extracellular matrix. Formation of the skeleton of the kype resembles antler development in deer (a form of regeneration), or hyperostotic bone formation in other teleost fishes, rather than periosteal bone growth. The type of boneformation may be understandable in the light of the animals' starvation and the energetic costs of upstream migration. However, the structured and regulated mode of bone formation suggests that the skeleton of the kype has functional relevance and is not a by-product of hormonal alterations or change of habitat

Chiral extrapolation beyond the power-counting regime

Chiral effective field theory can provide valuable insight into the chiral physics of hadrons when used in conjunction with non-perturbative schemes such as lattice QCD. In this discourse, the attention is focused on extrapolating the mass of the rho meson to the physical pion mass in quenched QCD (QQCD). With the absence of a known experimental value, this serves to demonstrate the ability of the extrapolation scheme to make predictions without prior bias. By using extended effective field theory developed previously, an extrapolation is performed using quenched lattice QCD data that extends outside the chiral power-counting regime (PCR). The method involves an analysis of the renormalization flow curves of the low energy coefficients in a finite-range regularized effective field theory. The analysis identifies an optimal regulator, which is embedded in the lattice QCD data themselves. This optimal regulator is the regulator value at which the renormalization of the low energy coefficients is approximately independent of the range of quark masses considered. By using recent precision, quenched lattice results, the extrapolation is tested directly by truncating the analysis to a set of points above 380 MeV, while being blinded of the results probing deeply into the chiral regime. The result is a successful extrapolation to the chiral regime.Comment: 8 pages, 18 figure

Universal geometric approach to uncertainty, entropy and information

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique "ensemble volume" is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon bounds in quantum and classical information theory; a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles; a geometric derivation of semi-classical uncertainty relations; a new means for defining classical and quantum localization for arbitrary evolution processes; a geometric interpretation of relative entropy; and a new proposed definition for the spot-size of an optical beam. Advantages of the ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10) of published version