3,068 research outputs found
Equivariant quantization of orbifolds
Equivariant quantization is a new theory that highlights the role of
symmetries in the relationship between classical and quantum dynamical systems.
These symmetries are also one of the reasons for the recent interest in
quantization of singular spaces, orbifolds, stratified spaces... In this work,
we prove existence of an equivariant quantization for orbifolds. Our
construction combines an appropriate desingularization of any Riemannian
orbifold by a foliated smooth manifold, with the foliated equivariant
quantization that we built in \cite{PoRaWo}. Further, we suggest definitions of
the common geometric objects on orbifolds, which capture the nature of these
spaces and guarantee, together with the properties of the mentioned foliated
resolution, the needed correspondences between singular objects of the orbifold
and the respective foliated objects of its desingularization.Comment: 13 page
Ab initio calculation of H + He charge transfer cross sections for plasma physics
The charge transfer in low energy (0.25 to 150 eV/amu) H() + He
collisions is investigated using a quasi-molecular approach for the as
well as the first two singlet states. The diabatic potential energy
curves of the HeH molecular ion are obtained from the adiabatic potential
energy curves and the non-adiabatic radial coupling matrix elements using a
two-by-two diabatization method, and a time-dependent wave-packet approach is
used to calculate the state-to-state cross sections. We find a strong
dependence of the charge transfer cross section in the principal and orbital
quantum numbers and of the initial or final state. We estimate the
effect of the non-adiabatic rotational couplings, which is found to be
important even at energies below 1 eV/amu. However, the effect is small on the
total cross sections at energies below 10 eV/amu. We observe that to calculate
charge transfer cross sections in a manifold, it is only necessary to
include states with , and we discuss the limitations of our
approach as the number of states increases.Comment: 14 pages, 10 figure
Critical parameters for the partial coalescence of a droplet
The partial coalescence of a droplet onto a planar liquid/liquid interface is
investigated experimentally by tuning the viscosities of both liquids. The
problem mainly depends on four dimensionless parameters: the Bond number
(gravity vs. surface tension), the Ohnesorge numbers (viscosity in both fluids
vs. surface tension), and the density relative difference. The ratio between
the daughter droplet size and the mother droplet size is investigated as a
function of these dimensionless numbers. Global quantities such as the
available surface energy of the droplet has been measured during the
coalescence. The capillary waves propagation and damping are studied in detail.
The relation between these waves and the partial coalescence is discussed.
Additional viscous mechanisms are proposed in order to explain the asymmetric
role played by both viscosities.Comment: 16 pages, 14 figures, submitted to Physical Review
A hermeneutic inquiry into user-created personas in different Namibian locales
Persona is a tool broadly used in technology design to support communicational interactions between designers and users. Different Persona types and methods have evolved mostly in the Global North, and been partially deployed in the Global South every so often in its original User-Centred Design methodology. We postulate persona conceptualizations are expected to differ across cultures. We demonstrate this with an exploratory-case study on user-created persona co-designed with four Namibian ethnic groups: ovaHerero, Ovambo, ovaHimba and Khoisan. We follow a hermeneutic inquiry approach to discern cultural nuances from diverse human conducts. Findings reveal diverse self-representations whereby for each ethnic group results emerge in unalike fashions, viewpoints, recounts and storylines. This paper ultimately argues User-Created Persona as a potentially valid approach for pursuing cross-cultural depictions of personas that communicate cultural features and user experiences paramount to designing acceptable and gratifying technologies in dissimilar locales
On sl(2)-equivariant quantizations
By computing certain cohomology of Vect(M) of smooth vector fields we prove
that on 1-dimensional manifolds M there is no quantization map intertwining the
action of non-projective embeddings of the Lie algebra sl(2) into the Lie
algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant
quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear
Mathematical Physic
Natural and projectively equivariant quantizations by means of Cartan Connections
The existence of a natural and projectively equivariant quantization in the
sense of Lecomte [20] was proved recently by M. Bordemann [4], using the
framework of Thomas-Whitehead connections. We give a new proof of existence
using the notion of Cartan projective connections and we obtain an explicit
formula in terms of these connections. Our method yields the existence of a
projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant
quantization exists in the flat situation in the sense of [18], thus solving
one of the problems left open by M. Bordemann.Comment: 13 page
Differential operators on supercircle: conformally equivariant quantization and symbol calculus
We consider the supercircle equipped with the standard contact
structure. The conformal Lie superalgebra K(1) acts on as the Lie
superalgebra of contact vector fields; it contains the M\"obius superalgebra
. We study the space of linear differential operators on weighted
densities as a module over . We introduce the canonical isomorphism
between this space and the corresponding space of symbols and find interesting
resonant cases where such an isomorphism does not exist
Chaotic properties of systems with Markov dynamics
We present a general approach for computing the dynamic partition function of
a continuous-time Markov process. The Ruelle topological pressure is identified
with the large deviation function of a physical observable. We construct for
the first time a corresponding finite Kolmogorov-Sinai entropy for these
processes. Then, as an example, the latter is computed for a symmetric
exclusion process. We further present the first exact calculation of the
topological pressure for an N-body stochastic interacting system, namely an
infinite-range Ising model endowed with spin-flip dynamics. Expressions for the
Kolmogorov-Sinai and the topological entropies follow.Comment: 4 pages, to appear in the Physical Review Letter
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