31,372 research outputs found
Higher-order supersymmetric quantum mechanics
We review the higher-order supersymmetric quantum mechanics (H-SUSY QM),
which involves differential intertwining operators of order greater than one.
The iterations of first-order SUSY transformations are used to derive in a
simple way the higher-order case. The second order technique is addressed
directly, and through this approach unexpected possibilities for designing
spectra are uncovered. The formalism is applied to the harmonic oscillator: the
corresponding H-SUSY partner Hamiltonians are ruled by polynomial Heisenberg
algebras which allow a straight construction of the coherent states.Comment: 42 pages, 12 eps figure
Deformations of complex structures and the coupled K\"ahler-Yang-Mills equations
In this work we define a deformation theory for the Coupled
K\"ahler-Yang-Mills equations in arXiv:1102.0991, generalizing work of
Sz\'ekelyhidi on constant scalar curvature K\"ahler metrics. We use the theory
to find new solutions of the equations via deformation of the complex structure
of a polarised manifold endowed with a holomorphic vector bundle. We also study
the deformations of the recent examples of Keller and T{\o}nnesen-Friedman.Comment: 19 page
Use of the fungal pathogen Hirsutella cryptosclerotium sp. nov. for the biocontrol of Rastrococcus invadens (Pseudococcidae)
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Perfect simulation for interacting point processes, loss networks and Ising models
We present a perfect simulation algorithm for measures that are absolutely
continuous with respect to some Poisson process and can be obtained as
invariant measures of birth-and-death processes. Examples include area- and
perimeter-interacting point processes (with stochastic grains), invariant
measures of loss networks, and the Ising contour and random cluster models. The
algorithm does not involve couplings of the process with different initial
conditions and it is not tied up to monotonicity requirements. Furthermore, it
directly provides perfect samples of finite windows of the infinite-volume
measure, subjected to time and space ``user-impatience bias''. The algorithm is
based on a two-step procedure: (i) a perfect-simulation scheme for a (finite
and random) relevant portion of a (space-time) marked Poisson processes (free
birth-and-death process, free loss networks), and (ii) a ``cleaning'' algorithm
that trims out this process according to the interaction rules of the target
process. The first step involves the perfect generation of ``ancestors'' of a
given object, that is of predecessors that may have an influence on the
birth-rate under the target process. The second step, and hence the whole
procedure, is feasible if these ``ancestors'' form a finite set with
probability one. We present a sufficiency criteria for this condition, based on
the absence of infinite clusters for an associated (backwards) oriented
percolation model.Comment: Revised version after referee of SPA: 39 page
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