Simplifying the spectral analysis of the volume operator

The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis, for quantum states that can be realized on a cubic three-dimensional lattice. This involves a decomposition of Hilbert space into sectors transforming according to the irreducible representations of a subgroup of the cubic group. As an application, we determine the complete spectrum for a class of states with six-valent intersections.Comment: 19 pages, TeX, to be published in Nucl. Phys.

Quantum groups, Yang-Baxter maps and quasi-determinants

For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang-Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum Yang-Baxter map, which satisfies the set-theoretic Yang-Baxter equation. The map has a zero curvature representation among L-operators defined as images of the universal R-matrix. We find that the zero curvature representation can be solved by the Gauss decomposition of a product of L-operators. Thereby obtained a quasi-determinant expression of the quantum Yang-Baxter map associated with the quantum algebra $U_{q}(gl(n))$. Moreover, the map is identified with products of quasi-Pl\"{u}cker coordinates over a matrix composed of the L-operators. We also consider the quasi-classical limit, where the underlying quantum algebra reduces to a Poisson algebra. The quasi-determinant expression of the quantum Yang-Baxter map reduces to ratios of determinants, which give a new expression of a classical Yang-Baxter map.Comment: 46 page

The 12CO/13CO ratio in AGB stars of different chemical type-Connection to the 12C/13C ratio and the evolution along the AGB

The aim of this paper is to investigate the evolution of the 12C/13C ratio along the AGB through the circumstellar 12CO/13CO ratio. This is the first time a sample including a significant number of M- and S-type stars is analysed together with a carbon-star sample of equal size, making it possible to investigate trends among the different types and establish evolutionary effects. The circumstellar 12CO/13CO abundance ratios are estimated through a detailed radiative transfer analysis of single-dish radio line emission observations. First, the 12CO radiative transfer is solved, assuming an abundance (dependent on the chemical type of the star), to give the physical parameters of the gas, i.e. mass-loss rate, gas expansion velocity, and gas temperature distribution. Then, the 13CO radiative transfer is solved using the results of the 12CO model giving the 13CO abundance. Finally, the 12CO/13CO abundance ratio is calculated. The circumstellar 12CO/13CO abundance ratio differs between the three spectral types. This is consistent with what is expected from stellar evolutionary models assuming that the spectral types constitute an evolutionary sequence; however, this is the first time this has been shown observationally for a relatively large sample covering all three spectral types. The median value of the 13CO abundance in the inner circumstellar envelope is 1.6x10^-5, 2.3x10^-5, and 3.0x10^-5 for the M-type, S-type, and carbon stars of the sample, respectively, corresponding to 12CO/13CO abundance ratios of 13, 26, and 34, respectively. Interestingly, the abundance ratio spread of the carbon stars is much larger than for the M- and S-type stars, even when excluding J-type carbon stars, in line with what could be expected from evolution on the AGB. We find no correlation between the isotopologue ratio and the mass-loss rate, as would be expected if both increase as the star evolves.Comment: 11 pages, 5 figures, accepted for publication in A&

Realization of universal nonadiabatic geometric control on decoherence-free qubits in the XY model

A fundamental requirement of quantum information processing is the protection from the adverse effects of decoherence and noise. Decoherence-free subspaces and geometric processing are important steps of quantum information protection. Here, we provide a new experimentally feasible scheme to combine decoherence-free subspaces with nonadiabatic geometric manipulations to attain a universal quantum computation. The proposed scheme is different from previous proposals and is based on the typical XY interaction coupling, which can be set up in various nano-engineered systems and therefore open up for realization of nonadiabatic holonomic quantum computation in decoherence-free subspaces.Comment: 21 pages, 5 figure

Flavour Mixing of Neutrinos and Baryon Asymmetry of the Universe

We investigate baryogenesis in the $\nu$MSM, which is the Minimal Standard Model (MSM) extended by three right-handed neutrinos with Majorana masses smaller than the weak scale. In this model the baryon asymmetry of the universe (BAU) is generated via flavour oscillation between right-handed neutrinos. We consider the case when BAU is solely originated from the CP violation in the mixing matrix of active neutrinos. We perform analytical and numerical estimations of the yield of BAU, and show how BAU depends on mixing angles and CP violating phases. It is found that the asymmetry in the inverted hierarchy for neutrino masses receives a suppression factor of about 4% comparing with the normal hierarchy case. It is, however, pointed out that, when $\theta_{13}=0$ and $\theta_{23} = \pi/4$, baryogenesis in the normal hierarchy becomes ineffective, and hence the inverted hierarchy case becomes significant to account for the present BAU.Comment: 15 pages, 7 figure

The Mini-Superspace Limit of the SL(2,C)/SU(2)-WZNW Model

Many qualitatively new features of WZNW models associated to noncompact cosets are due to zero modes with continuous spectrum. Insight may be gained by reducing the theory to its zero-mode sector, the mini-superspace limit. This will be discussed in some detail for the example of SL(2,C)/SU(2)-WZNW model. The mini-superspace limit of this model can be formulated as baby-CFT. Spectrum, structure constants and fusion rules as well as factorization of four point functions are obtained from the harmonic analysis on SL(2,C)/SU(2). The issues of operator-state correspondence or the appearance of non-normalizable intermediate states in correlation functions can be discussed transparently in this context.Comment: 17 pages, AMS-LATEX2e, minor correction

Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory

This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Stäckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems

The small scale dynamo and the amplification of magnetic fields in massive primordial haloes

While present standard model of cosmology yields no clear prediction for the initial magnetic field strength, efficient dynamo action may compensate for initially weak seed fields via rapid amplification. In particular, the small-scale dynamo is expected to exponentially amplify any weak magnetic field in the presence of turbulence. We explore whether this scenario is viable using cosmological magneto-hydrodynamics simulations modeling the formation of the first galaxies, which are expected to form in so-called atomic cooling halos with virial temperatures $\rm T_{vir} \geq 10^{4}$ K. As previous calculations have shown that a high Jeans resolution is needed to resolve turbulent structures and dynamo effects, our calculations employ resolutions of up to 128 cells per Jeans length. The presence of the dynamo can be clearly confirmed for resolutions of at least 64 cells per Jeans length, while saturation occurs at approximate equipartition with turbulent energy. As a result of the large Reynolds numbers in primordial galaxies, we expect saturation to occur at early stages, implying magnetic field strengths of \sim0.1 $\mu$G at densities of 10^4 cm^{-3}.Comment: Matches the accepted version to be appeared in MNRA