Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2)SU(2) and SO(3)SO(3) groups

We prove that each action of a compact matrix quantum group on a compact quantum space can be decomposed into irreducible representations of the group. We give the formula for the corresponding multiplicities in the case of the quotient quantum spaces. We describe the subgroups and the quotient spaces of quantum SU(2) and SO(3) groups.Comment: 30 pages (with very slight changes

Statistical thermodynamics for a non-commutative special relativity: Emergence of a generalized quantum dynamics

There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a space-time line element is defined using a trace. In the present paper, following the theory of Trace Dynamics, we construct a statistical thermodynamics for the non-commutative special relativity, and show that one arrives at a generalized quantum dynamics in which space and time are non-classical and have an operator status. In a future work, we will show how standard quantum theory on a classical space-time background is recovered from here.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1106.091

Analytical results for the confinement mechanism in QCD_3

We present analytical methods for investigating the interaction of two heavy quarks in QCD_3 using the effective action approach. Our findings result in explicit expressions for the static potentials in QCD_3 for long and short distances. With regard to confinement, our conclusion reflects many features found in the more realistic world of QCD_4.Comment: 24 pages, uses REVTe

Monte Carlo Quasi-Heatbath by approximate inversion

When sampling the distribution P(phi) ~ exp(-|A phi|^2), a global heatbath normally proceeds by solving the linear system A phi = eta, where eta is a normal Gaussian vector, exactly. This paper shows how to preserve the distribution P(phi) while solving the linear system with arbitrarily low accuracy. Generalizations are presented.Comment: 10 pages, 1 figure; typos corrected, reference added; version to appear in Phys. Rev.

Incremental verification of co-observability in discrete-event systems

Existing strategies for verifying co-observability, one of the properties that must be satisfied for synthesizing solutions to decentralized supervisory control problems, require the construction of the complete system model. When the system is composed of many subsystems, these monolithic approaches may be impractical due to the state-space explosion problem. To address this issue, we introduce an incremental verification of co-observability approach. Selected subgroups of the system are evaluated individually, until verification of co-observability is complete. The new method is potentially much more efficient than the monolithic approaches, in particular for systems composed of many subsystems, allowing for some intractable state-space explosion problems to be manageable. Properties of this new strategy are presented, along with a corresponding algorithm and an example

The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifold

A generic geodesic on a finite area, hyperbolic 2-orbifold exhibits an infinite sequence of penetrations into a neighborhood of a cone singularity, so that the sequence of depths of maximal penetration has a limiting distribution. The distribution function is the same for all such surfaces and is described by a fairly simple formula.Comment: 20 page

Exploring the Lewis basicity of the metalloligand [Pt₂(μ-Se)₂(PPh₃)₄] on metal substrates by electrospray mass spectrometry. Synthesis, characterization and structural studies of new platinum selenido phosphine complexes containing the {Pt₂Se₂} core

Electrospray Mass Spectrometry (ESMS) has been used as a tool to probe the reactivity of the metalloligand [Pt₂(μ-Se)₂(PPh₃)₄] with metal substrates, which lead to the formation of charged coordination complexes via loss of halides or other labile ligands. Among the numerous metal substrates used in the displacement reactions are Au(anpy)Cl₂ (anpy = cyclometallated 2-anilinopyridyl), HgPhCl and Pb(NO₃)₂. Acid titration on the Lewis basic metalloligand leads to the identification and isolation of the doubly-protonated species, [Pt₂(μ-SeH)₂(PPh₃)₄]²⁺, whose sulfide analogue cannot be isolated. A three-step strategy is employed in the use of ESMS as a probe: (i) preliminary screening of the metalloligand with an array of acidic main group and transition group metal compounds, (ii) identification of potentially stable and isolable products formed in situ based on ion distribution and simulated isotope patterns and (iii) promising reactions are repeated on a laboratory scale, and target products are isolated and characterized. X-Ray diffraction studies have been performed on single crystals of [Pt₂(μ-SeH)₂(PPh₃)₄][ClO₄]₂, [Pt₂(μ₃-Se)₂(PPh₃)₄(CdCl₂)] and {Pt₂(μ₃-Se)₂(PPh₃)₄[Pb(NO₃)]}{NO₃}. These results suggested that in general a parallel chemistry can be developed on the intermetallic selenides as on the sulfides. However, there are chemical and structural differences which are highlighted in this paper

Weak force detection with superposed coherent states

We investigate the utility of non classical states of simple harmonic oscillators, particularly a superposition of coherent states, for sensitive force detection. We find that like squeezed states a superposition of coherent states allows displacement measurements at the Heisenberg limit. Entangling many superpositions of coherent states offers a significant advantage over a single mode superposition states with the same mean photon number.Comment: 6 pages, no figures: New section added on entangled resources. Changes to discussions and conclusio

Matter-induced vertices for photon splitting in a weakly magnetized plasma

We evaluate the three-photon vertex functions at order $B$ and $B^{2}$ in a weak constant magnetic field at finite temperature and density with on shell external lines. Their application to the study of the photon splitting process leads to consider high energy photons whose dispersion relations are not changed significantly by the plasma effects. The absorption coefficient is computed and compared with the perturbative vacuum result. For the values of temperature and density of some astrophysical objects with a weak magnetic field, the matter effects are negligible.Comment: 14 pages, 1 figure. Accepted for publication in PR

Minimum Particle Size for Cyclone Dust Separator

Perkins technology wish to separate small soot particles from exhaust gases, and the question posed to the study group was to determine the feasibility of using a cyclone separator to remove these particles. Soot is mostly composed of polycyclicaromatic compounds and results from the incomplete combustion of the diesel fuel in the engine. The average size of the particles formed in the engine is in the range 3 to 10 nm in diameter, but this is known to increase within the exhaust system. In the first part of this report we determine the minimum particle size that can be removed by centrifugal separation. The second part discusses the mechanisms for particle growth within the exhaust system in order to estimate the particle growth rate. In section two we estimate the minimum particle diameter that can be removed by a cyclone separator is around one micron. This estimate is consistent with current applications of hydrocyclones. The particle size measurements by Perkins Technology together with our estimates from section three, suggest that the soot particles are an order of magnitude smaller than this. Although it may be possible to remove some particles less than one micron in diameter with a well designed high-speed cyclone, we do not think it will be possible to remove a substantial proportion of 100 nm or smaller particles. The growth rate of the particles increases if the particles volume fraction or the polydispersity is increased. Therefore aggregation could be enhanced by the addition of larger particles (d > 1 µm) or water droplets (provided the water does not all vapourise) to the exhaust gas