31,006 research outputs found
The subgroup growth spectrum of virtually free groups
For a finitely generated group denote by the growth
coefficient of , that is, the infimum over all real numbers such
that . We show that the growth coefficient of a virtually
free group is always rational, and that every rational number occurs as growth
coefficient of some virtually free group. Moreover, we describe an algorithm to
compute
The locality of the square-root method for improved staggered quarks
We study the effects of improvement on the locality of square-rooted
staggered Dirac operators in lattice QCD simulations. We find the localisation
lengths of the improved operators (FAT7TAD and ASQTAD) to be very similar to
that of the one-link operator studied by Bunk et al., being at least the
Compton wavelength of the lightest particle in the theory, even in the
continuum limit. We conclude that improvement has no effect. We discuss the
implications of this result for the locality of the nth-rooted fermion
determinant used to reduce the number of sea quark flavours, and for possible
staggered valence quark formulations
Asymptotics of relative heat traces and determinants on open surfaces of finite area
The goal of this paper is to prove that on surfaces with asymptotically cusp
ends the relative determinant of pairs of Laplace operators is well defined. We
consider a surface with cusps (M,g) and a metric h on the surface that is a
conformal transformation of the initial metric g. We prove the existence of the
relative determinant of the pair under suitable
conditions on the conformal factor. The core of the paper is the proof of the
existence of an asymptotic expansion of the relative heat trace for small
times. We find the decay of the conformal factor at infinity for which this
asymptotic expansion exists and the relative determinant is defined. Following
the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of
determinants on compact surfaces, we prove Polyakov's formula for the relative
determinant and discuss the extremal problem inside a conformal class. We
discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51
page
Butterfly hysteresis loop and dissipative spin reversal in the S=1/2, V15 molecular complex
Time resolved magnetization measurements have been performed on a spin 1/2
molecular complex, so called V. Despite the absence of a barrier,
magnetic hysteresis is observed over a timescale of several seconds. A detailed
analysis in terms of a dissipative two level model is given, in which
fluctuations and splittings are of same energy. Spin-phonon coupling leads to
long relaxation times and to a particular "butterfly" hysteresis loop.Comment: LaTeX/RevTeX, 3 figures.Approved for publication in PR
Invertible Dirac operators and handle attachments on manifolds with boundary
For spin manifolds with boundary we consider Riemannian metrics which are
product near the boundary and are such that the corresponding Dirac operator is
invertible when half-infinite cylinders are attached at the boundary. The main
result of this paper is that these properties of a metric can be preserved when
the metric is extended over a handle of codimension at least two attached at
the boundary. Applications of this result include the construction of
non-isotopic metrics with invertible Dirac operator, and a concordance
existence and classification theorem.Comment: Accepted for publication in Journal of Topology and Analysi
Three-dimensional elastic deformation of functionally graded isotropic plates under point loading
Acknowledgement Financial support of this research by The Royal Society (UK) under grant number JP090633 is gratefully acknowledged.Peer reviewedPostprin
Parallel tempering in full QCD with Wilson fermions
We study the performance of QCD simulations with dynamical Wilson fermions by
combining the Hybrid Monte Carlo algorithm with parallel tempering on
and lattices. In order to compare tempered with standard simulations,
covariance matrices between sub-ensembles have to be formulated and evaluated
using the general properties of autocorrelations of the parallel tempering
algorithm. We find that rendering the hopping parameter dynamical does
not lead to an essential improvement. We point out possible reasons for this
observation and discuss more suitable ways of applying parallel tempering to
QCD.Comment: 16 pages, 3 figure
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