68,374 research outputs found
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Representations of wreath products of algebras
Filtrations of modules over wreath products of algebras are studied and corresponding multiplicity formulas are given in terms of Littlewood–Richardson coefficients. An example relevant to Jantzen filtrations in Schur algebras is presented
Smooth critical points of planar harmonic mappings
In a work in 1992, Lyzzaik studies local properties of light harmonic
mappings. More precisely, he classifies their critical points and accordingly
studies their topological and geometrical behaviours. We will focus our study
on smooth critical points of light harmonic maps. We will establish several
relationships between miscellaneous local invariants, and show how to connect
them to Lyzzaik's models. With a crucial use of Milnor fibration theory, we get
a fundamental and yet quite unexpected relation between three of the numerical
invariants, namely the complex multiplicity, the local order of the map and the
Puiseux pair of the critical value curve. We also derive similar results for a
real and complex analytic planar germ at a regular point of its Jacobian
level-0 curve. Inspired by Whitney's work on cusps and folds, we develop an
iterative algorithm computing the invariants. Examples are presented in order
to compare the harmonic situation to the real analytic one.Comment: 36 pages, 5 figure
Recommended from our members
Kleshchev's decomposition numbers and branching coefficients in the Fock space
10.1090/S0002-9947-07-04202-XTransactions of the American Mathematical Society36031179-119
A heterotic sigma model with novel target geometry
We construct a (1,2) heterotic sigma model whose target space geometry
consists of a transitive Lie algebroid with complex structure on a Kaehler
manifold. We show that, under certain geometrical and topological conditions,
there are two distinguished topological half--twists of the heterotic sigma
model leading to A and B type half--topological models. Each of these models is
characterized by the usual topological BRST operator, stemming from the
heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with
the former, originating from the (1,0) supersymmetry. These BRST operators
combined in a certain way provide each half--topological model with two
inequivalent BRST structures and, correspondingly, two distinct perturbative
chiral algebras and chiral rings. The latter are studied in detail and
characterized geometrically in terms of Lie algebroid cohomology in the
quasiclassical limit.Comment: 83 pages, no figures, 2 references adde
Exciton and biexciton energies in bilayer systems
We report calculations of the energies of excitons and biexcitons in ideal
two-dimensional bilayer systems within the effective-mass approximation with
isotropic electron and hole masses. The exciton energies are obtained by a
simple numerical integration technique, while the biexciton energies are
obtained from diffusion quantum Monte Carlo calculations. The exciton binding
energy decays as the inverse of the separation of the layers, while the binding
energy of the biexciton with respect to dissociation into two separate excitons
decays exponentially
Short-range correlations in dilute atomic Fermi gases with spin-orbit coupling
We study the short-range correlation strength of three dimensional spin half
dilute atomic Fermi gases with spin-orbit coupling. The interatomic interaction
is modeled by the contact pseudopotential. In the high temperature limit, we
derive the expression for the second order virial expansion of the
thermodynamic potential via the ladder diagrams. We further evaluate the second
order virial expansion in the limit that the spin-orbit coupling constants are
small, and find that the correlation strength between the fermions increases as
the forth power of the spin-orbit coupling constants. At zero temperature, we
consider the cases in which there are symmetric spin-orbit couplings in two or
three directions. In such cases, there is always a two-body bound state of zero
net momentum. In the limit that the average interparticle distance is much
larger than the dimension of the two-body bound state, the system primarily
consists of condensed bosonic molecules that fermions pair to form; we find
that the correlation strength also becomes bigger compared to that in the
absence of spin-orbit coupling. Our results indicate that generic spin-orbit
coupling enhances the short-range correlations of the Fermi gases. Measurement
of such enhancement by photoassociation experiment is also discussed.Comment: 7 pages, 4 figure
Studies of local magnetism and local structure in La(2-x)Sr(x)CuO4
The muon spin rotation (MUSR) study of local magnetism of Sr-doped La2CrO4 is reviewed. Emphasis is placed on magnetic order as detected by local and bulk probes with local atomic environments studies by x ray absorption fine structure (XAFS). Correlations between the MUSR study of local magnetic ordering and the bulk magnetization study are presented along with a discussion of the dependence upon oxygen stoichiometry. Results are presented for both superconducting phases and magnetic phases. Recent data which reveals the existence of local magnetic ordering in the hydrogen-doped YBa2Cu3O7 system are also discussed
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