The subgroup growth spectrum of virtually free groups

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. 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 $\mu$

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 $(\Delta_{h},\Delta_{g})$ 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$_{15}$. 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 $10^4$ and $12^4$ 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 $\kappa$ 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