Discrete Q- and P-symbols for spin s

Non-orthogonal bases of projectors on coherent states are introduced to expand Hermitean operators acting on the Hilbert space of a spin s. It is shown that the expectation values of a Hermitean operator (A) over cap in a family of (2s + 1)(2) spin-coherent states determine the operator unambiguously. In other words, knowing the Q-symbol of (A) over cap at (2s + 1)(2) points on the unit sphere is already sufficient in order to recover the operator. This provides a straightforward method to reconstruct the mixed state of a spin since its density matrix is explicitly parametrized in terms of expectation values. Furthermore, a discrete P-symbol emerges naturally which is related to a basis dual to the original one

Coherent states and the reconstruction of pure spin states

Coherent states provide an appealing method to reconstruct efficiently the pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s + 1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeros of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stem-Gerlach apparatus. This result comes down to saying that it is possible to resolve experimentally structures in quantum phase space which are smaller than (h) over bar

Contracting the Wigner kernel of a spin to the Wigner kernel of a particle

A general relation between the Moyal formalisms for a spin and a particle is established. Once the formalism has been set up for a spin, the phase-space description of a particle is obtained from contracting the group of rotations to the oscillator group. In this process, turn into a spin Wigner kernel turns into the Wigner kernel of a particle. In fact, only one out of 22s different possible kernels for a spin shows this behavior

Reconstructing a pure state of a spin s through three Stern-Gerlach measurements: II

The density matrix of a spin s is fixed uniquely if the probabilities to obtain the value s upon measuring n.S are known for 4s(s+1) appropriately chosen directions n in space. These numbers are just the expectation values of the density operator in coherent spin states, and they can be determined in an experiment carried out with a Stern-Gerlach apparatus. Furthermore, the experimental data can be inverted providing thus a parametrization of the statistical operator by 4s(s+1) positive parameters

Scattering in PT-symmetric quantum mechanics

A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with hermiticity, T invariance and PT invariance.Comment: 41 pages, to appear in Ann. Phy

Bose--Einstein Condensation and Thermalization of the Quark Gluon Plasma

In ultra-relativistic heavy ion collisions, the matter formed shortly after the collision is a dense, out of equilibrium, system of gluons characterized by a semi-hard momentum scale $Q_{\rm s}$. Simple power counting arguments indicate that this system is over-occupied: the gluon occupation number is parametrically large when compared to a system in thermal equilibrium with the same energy density. On short time scales, soft elastic scatterings tend to drive the system towards the formation of a Bose--Einstein condensate that contains a large fraction of the gluons while contributing little to the energy density. The lifetime and existence of this condensate depends on whether inelastic processes, that occur on the same time scale as the elastic ones, preferably increase or decrease the number of gluons. During this overpopulated stage, and all the way to thermalization, the system behaves as a strongly interacting fluid, even though the elementary coupling constant is small. We argue that while complete isotropization may never be reached, the system may yet evolve for a long time with a fixed anisotropy between average longitudinal and transverse momenta.Comment: 19 pages, 1 figure, v2 is a substantial re-write aimed at clarifying the presentation. Major arguments essentially unchanged, except in the discussion of inelastic processe

SNM Practice Guideline for Breast Scintigraphy with Breast-Specific gamma-Cameras 1.0

The intention of this guideline is to assist breast imaging practitioners in selecting patients for, performing, interpreting, and reporting 99mTc-sestamibi breast-specific γ-imaging

Fotodegradação de corante textil azul RB 250 e produção Fotocatalítica de H2 utilizando TiO2 Nano suportado em Zeolita ZSM-5 / RB 250 blue dye photodegradation and H2 Photocatalytic production using TiO2 Nano supported on Zeolite ZSM-5

Os processos oxidativos avançados (POAs) são uma alternativa promissora para o tratamento de efluente têxteis, principalmente se combinado a produção fotocatalítica de hidrogênio. O objetivo deste trabalho foi a  aplicação da fotocatálise heterogênea no tratamento do efluente têxtil sintético e posterior produção fotocatalítica de hidrogênio utilizando radiação artificial UV, utilizando como catalisador TiO2 nano particulado, suportados na zeólita ZSM-5 com 5 e 10% de fase ativa. Os catalisadores suportados foram caracterizados para identificação das propriedades texturais, estruturais e morfológicas, esses foram utilizados na degradação fotocatalítica do corante azul reativo RB250 no reator em batelada com reciclo e para produção de hidrogênio no reator em batelada. Os fotocatalisadores que apresentaram apresentaram descoloração do corante em 100% nos primeiros minutos de reação. A mineralização do efluente foi avaliada  e como todos os catalisadores foi obtido mineralização superior a 80%. Na produção de H2 o catalisador puro comercial se mostrou ser mais eficiente ques os catalisadores suportados na zeólita, obetendo uma produção de 11.05 µmol H2.gcat-1 sendo 50% mais eficiente que os catalisadores com 5 e 10% de fase ativa, os quais apresentaram um perfil de produção bastante próximos

Photocatalytic water splitting with noble-metal free cocatalysts for a comprehensive study of two nonidentical photoreactors designs

Here, the authors (i) discuss the most prominent co-catalyst for H2 generation struc tured in the form of Me-TiO2/MCM-41 (Me: Ag, Co, Cu, Ni) based on structural, electronic, textural, morphological and optical characterization techniques, such as XRD, wide and small angle, XPS, Fourier-transform infrared spectroscopy, scanning electron microscopy, B.E.T., textural analysis, photoacoustic spectroscopy and photo luminescence spectroscopy; and (ii) evaluate the difference in hydrogen production in two distinct geometric reactors based on a theoretical study of light distribution inside the reactors supported by the experimental quantum yield calculation. As a result, copper-doped photocatalyst generated higher hydrogen amount compared to the others. The high photocatalyst performance was due to the greater lamp spec trum absorption, marked by the low bandgap value, and high photoactivity justified by the low rate of electronic recombination. The hydrogen generation in the quartz reactor was seven times higher than the annular one, and when at maximum light power, it is comparable to the most sophisticated reaction systems found in litera ture. The larger light exposure area per unit volume of the quartz reactor compared to the annular one is the reason why it obtained better results due to the lower emit ted photon blockade, with a 1.81% apparent quantum yield