17,101 research outputs found
Counting (3+1) - Avoiding permutations
A poset is {\it (\3+\1)-free} if it contains no induced subposet isomorphic
to the disjoint union of a 3-element chain and a 1-element chain. These posets
are of interest because of their connection with interval orders and their
appearance in the (\3+\1)-free Conjecture of Stanley and Stembridge. The
dimension 2 posets are exactly the ones which have an associated
permutation where in if and only if as integers and
comes before in the one-line notation of . So we say that a
permutation is {\it (\3+\1)-free} or {\it (\3+\1)-avoiding} if its
poset is (\3+\1)-free. This is equivalent to avoiding the permutations
2341 and 4123 in the language of pattern avoidance. We give a complete
structural characterization of such permutations. This permits us to find their
generating function.Comment: 17 page
Some implications of changing the tax basis for pension funds
Governments in many developed economies provide private pension plans with significant taxation incentives. However, as many retirement income systems are now being reviewed due to demographic, social and economic pressures, these taxation arrangements are also under scrutiny. This paper discusses some of the implications of the differences between the traditional taxation treatment adopted by most OECD nations and that adopted by Australia, where there is a tax on contributions, a tax on investment earnings and a tax on benefits. The results show that there are significant differences in the net value of the benefits received by individuals and the taxation revenue received by the government. On the other hand, it is shown that there is remarkably little to distinguish between the two tax structures in terms of summary measures of lifetime income, although the form in which the benefit is taken in retirement is significant in influencing intragenerational equity.
Many-Impurity Effects in Fourier Transform Scanning Tunneling Spectroscopy
Fourier transform scanning tunneling spectroscopy (FTSTS) is a useful
technique for extracting details of the momentum-resolved electronic band
structure from inhomogeneities in the local density of states due to
disorder-related quasiparticle scattering. To a large extent, current
understanding of FTSTS is based on models of Friedel oscillations near isolated
impurities. Here, a framework for understanding many-impurity effects is
developed based on a systematic treatment of the variance Delta rho^2(q,omega)
of the Fourier transformed local density of states rho(q,\omega). One important
consequence of this work is a demonstration that the poor signal-to-noise ratio
inherent in rho(q,omega) due to randomness in impurity positions can be
eliminated by configuration averaging Delta rho^2(q,omega). Furthermore, we
develop a diagrammatic perturbation theory for Delta rho^2(q,omega) and show
that an important bulk quantity, the mean-free-path, can be extracted from
FTSTS experiments.Comment: 7 pages, 5 figures. A version of the paper with high resolution,
colour figures is available at
http://www.trentu.ca/physics/batkinson/FTSTS.ps.gz minor revisions in
response to refree report + figure 5 is modifie
Quantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization
We focus on determining the separability of an unknown bipartite quantum
state by invoking a sufficiently large subset of all possible
entanglement witnesses given the expected value of each element of a set of
mutually orthogonal observables. We review the concept of an entanglement
witness from the geometrical point of view and use this geometry to show that
the set of separable states is not a polytope and to characterize the class of
entanglement witnesses (observables) that detect entangled states on opposite
sides of the set of separable states. All this serves to motivate a classical
algorithm which, given the expected values of a subset of an orthogonal basis
of observables of an otherwise unknown quantum state, searches for an
entanglement witness in the span of the subset of observables. The idea of such
an algorithm, which is an efficient reduction of the quantum separability
problem to a global optimization problem, was introduced in PRA 70 060303(R),
where it was shown to be an improvement on the naive approach for the quantum
separability problem (exhaustive search for a decomposition of the given state
into a convex combination of separable states). The last section of the paper
discusses in more generality such algorithms, which, in our case, assume a
subroutine that computes the global maximum of a real function of several
variables. Despite this, we anticipate that such algorithms will perform
sufficiently well on small instances that they will render a feasible test for
separability in some cases of interest (e.g. in 3-by-3 dimensional systems)
Rapidly-converging methods for the location of quantum critical points from finite-size data
We analyze in detail, beyond the usual scaling hypothesis, the finite-size
convergence of static quantities toward the thermodynamic limit. In this way we
are able to obtain sequences of pseudo-critical points which display a faster
convergence rate as compared to currently used methods. The approaches are
valid in any spatial dimension and for any value of the dynamic exponent. We
demonstrate the effectiveness of our methods both analytically on the basis of
the one dimensional XY model, and numerically considering c = 1 transitions
occurring in non integrable spin models. In particular, we show that these
general methods are able to locate precisely the onset of the
Berezinskii-Kosterlitz-Thouless transition making only use of ground-state
properties on relatively small systems.Comment: 9 pages, 2 EPS figures, RevTeX style. Updated to published versio
On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model
We investigate the quantum Jaynes-Cummings model - a particular case of the
Gaudin model with one of the spins being infinite. Starting from the Bethe
equations we derive Baxter's equation and from it a closed set of equations for
the eigenvalues of the commuting Hamiltonians. A scalar product in the
separated variables representation is found for which the commuting
Hamiltonians are Hermitian. In the semi classical limit the Bethe roots
accumulate on very specific curves in the complex plane. We give the equation
of these curves. They build up a system of cuts modeling the spectral curve as
a two sheeted cover of the complex plane. Finally, we extend some of these
results to the XXX Heisenberg spin chain.Comment: 16 page
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