Non-uniqueness of the Dirac theory in a curved spacetime

We summarize a recent work on the subject title. The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields leads to an equivalent Hamiltonian operator H, or to an equivalent energy operator E. In this paper, we focus on the standard version of the gravitational Dirac equation, but the non-uniqueness applies also to our alternative versions. We find that the changes which lead to an equivalent operator H, or respectively to an equivalent operator E, are determined by initial data, or respectively have to make some point-dependent antihermitian matrix vanish. Thus, the vast majority of the possible coefficient changes lead neither to an equivalent operator H, nor to an equivalent operator E, whence a lack of uniqueness. We show that even the Dirac energy spectrum is not unique.Comment: 13 pages (standard 12pt article format). Text of a talk given at the 1st Mediterranean Conference on Classical and Quantum Gravity, Kolymbari (Greece), Sept. 14-18, 200

Long range coherent magnetic bound states in superconductors

The quantum coherent coupling of completely different degrees of freedom is a challenging path towards creating new functionalities for quantum electronics. Usually the antagonistic coupling between spins of magnetic impurities and superconductivity leads to the destruction of the superconducting order. Here we show that a localized classical spin of an iron atom immersed in a superconducting condensate can give rise to new kind of long range coherent magnetic quantum state. In addition to the well-known Shiba bound state present on top of an impurity we reveal the existence of a star shaped pattern which extends as far as 12 nm from the impurity location. This large spatial dispersion turns out to be related, in a non-trivial way, to the superconducting coherence length. Inside star branches we observed short scale interference fringes with a particle-hole asymmetry. Our theoretical approach captures these features and relates them to the electronic band structure and the Fermi wave length of the superconductor. The discovery of a directional long range effect implies that distant magnetic atoms could coherently interact leading to new topological superconducting phases with fascinating properties

On irreducibility of tensor products of evaluation modules for the quantum affine algebra

Every irreducible finite-dimensional representation of the quantized enveloping algebra U_q(gl_n) can be extended to the corresponding quantum affine algebra via the evaluation homomorphism. We give in explicit form the necessary and sufficient conditions for irreducibility of tensor products of such evaluation modules.Comment: 22 pages. Some references are adde

Completely splittable representations of affine Hecke-Clifford algebras

We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.Comment: 39 pages, v2, added a new reference with comments in section 4.4, added two examples (Example 5.4 and Example 5.11) in section 5, mild corrections of some typos, to appear in J. Algebraic Combinatoric

Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation

We present a simple method to derive the semiclassical equations of motion for a spinning particle in a gravitational field. We investigate the cases of classical, rotating particles (pole-dipole particles), as well as particles with intrinsic spin. We show that, starting with a simple Lagrangian, one can derive equations for the spin evolution and momentum propagation in the framework of metric theories of gravity and in theories based on a Riemann-Cartan geometry (Poincare gauge theory), without explicitly referring to matter current densities (spin and energy-momentum). Our results agree with those derived from the multipole expansion of the current densities by the conventional Papapetrou method and from the WKB analysis for elementary particles.Comment: 28 page

Evaluation of the Atlas of Honduras (Atlas Mitch)

In October 1998, the Seeds of Hope project contributed to the production of 2,000 copies of the “Mitch Atlas”, containing fundamental maps on population, land use, roads, rivers, topography, and soils. The Atlas was freely distributed to institutions for post-Hurricane Mitch emergency response and reconstruction. Two years later, the Seeds of Hope project conducted an impact assessment of the Atlas in order to gauge the role of geographic information on decision-making. The results of this impact assessment are presented in this report. The methods used to assess the impact of the Atlas combined case study analysis and descriptive statistics. We interviewed 20 Atlas users and received 43 completed questionnaires. Based on user responses, the Atlas of Honduras made a significant contribution to disaster response, agricultural development, and natural resource management in Honduras. Overall, 97.7% of the respondents said they thought the Atlas was a useful tool, and 84.8% thought the Atlas was the best compilation of geographic information available in Honduras. Seventy four percent of the respondents found the Atlas easy to use, and 90.5% used the Atlas interface itself, rather than copying the data to be used with their own GIS software. This indicates that the interface itself was well designed. The Atlas was used for a range of applications, from basic mapping to more strategic planning, predominantly within the agricultural and natural resources management sectors. Nearly all those who participated in this evaluation indicated that the Atlas improved the quality and efficiency of decision-making. However, a number of Atlas users mentioned that the Atlas was one of a range of tools and information sources, so they were reluctant to assert that the Atlas had a direct impact on their decision-making. The Atlas was instrumental in raising awareness of the value of geographic information and need to share information. With the Atlas now 2 years old, 100% of the users sampled expressed an interest in having an updated version produced, and 92.7% said they would be willing to contribute to it. 88.1% of the sampled users said they expect to use geographic information frequently in the next five years, indicating that geographic information will have a prominent role in the future

Fermionic realization of two-parameter quantum affine algebra Ur,s(sln)U_{r,s}({sl_n})

We construct all fundamental modules for the two parameter quantum affine algebra of type $A$ using a combinatorial model of Young diagrams. In particular we also give a fermionic realization of the two-parameter quantum affine algebra

INVOLVEMENT OF RESPIRATORY CHAIN IN BIOFILM FORMATION IN PORPHYROMONAS GINGIVALIS

Oral Communication presented at the ";Forum des Jeunes Chercheurs";, Brest (France) 2011

Minimum triplet covers of binary phylogenetic X-trees

Trees with labelled leaves and with all other vertices of degree three play an important role in systematic biology and other areas of classification. A classical combinatorial result ensures that such trees can be uniquely reconstructed from the distances between the leaves (when the edges are given any strictly positive lengths). Moreover, a linear number of these pairwise distance values suffices to determine both the tree and its edge lengths. A natural set of pairs of leaves is provided by any `triplet cover' of the tree (based on the fact that each non-leaf vertex is the median vertex of three leaves). In this paper we describe a number of new results concerning triplet covers of minimum size. In particular, we characterize such covers in terms of an associated graph being a 2-tree. Also, we show that minimum triplet covers are `shellable' and thereby provide a set of pairs for which the inter-leaf distance values will uniquely determine the underlying tree and its associated branch lengths