13,647 research outputs found
Equivariant K-theory of compact Lie group actions with maximal rank isotropy
Let G denote a compact connected Lie group with torsion-free fundamental
group acting on a compact space X such that all the isotropy subgroups are
connected subgroups of maximal rank. Let be a maximal torus with
Weyl group W. If the fixed-point set has the homotopy type of a finite
W-CW complex, we prove that the rationalized complex equivariant K-theory of X
is a free module over the representation ring of G. Given additional conditions
on the W-action on the fixed-point set we show that the equivariant
K-theory of X is free over R(G). We use this to provide computations for a
number of examples, including the ordered n-tuples of commuting elements in G
with the conjugation action.Comment: Accepted for publication by the Journal of Topolog
Three-body bound states in a lattice
We pursue three-body bound states in a one-dimensional tight-binding lattice
described by the Bose-Hubbard model with strong on-site interaction. Apart from
the simple strongly-bound "trimer" state corresponding to all three particles
occupying the same lattice site, we find two novel kinds of weakly-bound
trimers with energies below and above the continuum of scattering states of a
single particle ("monomer") and a bound particle pair ("dimer"). The
corresponding binding mechanism can be inferred from an effective Hamiltonian
in the strong-coupling regime which contains an exchange interaction between
the monomer and dimer. In the limit of very strong on-site interaction, the
exchange-bound trimers attain a universal value of the binding energy. These
phenomena can be observed with cold atoms in optical lattices
Towards an Abstract Domain for Resource Analysis of Logic Programs Using Sized Types
We present a novel general resource analysis for logic programs based on
sized types.Sized types are representations that incorporate structural (shape)
information and allow expressing both lower and upper bounds on the size of a
set of terms and their subterms at any position and depth. They also allow
relating the sizes of terms and subterms occurring at different argument
positions in logic predicates. Using these sized types, the resource analysis
can infer both lower and upper bounds on the resources used by all the
procedures in a program as functions on input term (and subterm) sizes,
overcoming limitations of existing analyses and enhancing their precision. Our
new resource analysis has been developed within the abstract interpretation
framework, as an extension of the sized types abstract domain, and has been
integrated into the Ciao preprocessor, CiaoPP. The abstract domain operations
are integrated with the setting up and solving of recurrence equations for
both, inferring size and resource usage functions. We show that the analysis is
an improvement over the previous resource analysis present in CiaoPP and
compares well in power to state of the art systems.Comment: Part of WLPE 2013 proceedings (arXiv:1308.2055
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