Lattice QCD at non-vanishing density: phase diagram, equation of state

We propose a method to study lattice QCD at non-vanishing temperature (T) and chemical potential (\mu). We use n_f=2+1 dynamical staggered quarks with semi-realistic masses on L_t=4 lattices. The critical endpoint (E) of QCD on the Re(\mu)-T plane is located. We calculate the pressure (p), the energy density (\epsilon) and the baryon density (n_B) of QCD at non-vanishing T and \mu.Comment: Contributed to Workshop on Strong and Electroweak Matter (SEWM 2002), Heidelberg, Germany, 2-5 Oct 200

The QCD equation of state at finite T/\mu on the lattice

We present N_t=4 lattice results for the equation of state of 2+1 flavour staggered, dynamical QCD at finite temperature and chemical potential. We use the overlap improving multi-parameter reweighting technique to extend the equation of state for non-vanishing chemical potentials. The results are obtained along the line of constant physics. Our physical parameters extend in temperature and baryon chemical potential upto \approx 500-600 MeV.Comment: 13 pages 9 figures, talk given at Finite Density QCD at Nara, Nara, Japan, 10-12 July 200

Maximum likelihood estimates of pairwise rearrangement distances

Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. In the case of bacteria, distances can be estimated using a range of different evolutionary models, from single nucleotide polymorphisms to large-scale genome rearrangements. In the case of sequence evolution models (such as the Jukes-Cantor model and associated metric) have been used to correct pairwise distances. Similar correction methods for genome rearrangement processes are required to improve inference. Current attempts at correction fall into 3 categories: Empirical computational studies, Bayesian/MCMC approaches, and combinatorial approaches. Here we introduce a maximum likelihood estimator for the inversion distance between a pair of genomes, using the group-theoretic approach to modelling inversions introduced recently. This MLE functions as a corrected distance: in particular, we show that because of the way sequences of inversions interact with each other, it is quite possible for minimal distance and MLE distance to differently order the distances of two genomes from a third. This has obvious implications for the use of minimal distance in phylogeny reconstruction. The work also tackles the above problem allowing free rotation of the genome. Generally a frame of reference is locked, and all computation made accordingly. This work incorporates the action of the dihedral group so that distance estimates are free from any a priori frame of reference.Comment: 21 pages, 7 figures. To appear in the Journal of Theoretical Biolog

Computing finite semigroups

Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids, matrix semigroups, and subsemigroups of finite regular Rees matrix and 0-matrix semigroups over groups. For any subsemigroup of such a semigroup, it is possible to, among other things, efficiently compute its size and Green's relations, test membership, factorize elements over the generators, find the semigroup generated by the given subsemigroup and any collection of additional elements, calculate the partial order of the D-classes, test regularity, and determine the idempotents. This is achieved by representing the given subsemigroup without exhaustively enumerating its elements. It is also possible to compute the Green's classes of an element of such a subsemigroup without determining the global structure of the semigroup.PreprintPostprintPeer reviewe

Topology with Dynamical Overlap Fermions

We perform dynamical QCD simulations with $n_f=2$ overlap fermions by hybrid Monte-Carlo method on $6^4$ to $8^3\times 16$ lattices. We study the problem of topological sector changing. A new method is proposed which works without topological sector changes. We use this new method to determine the topological susceptibility at various quark masses.Comment: 15 pages, 3 figure

Lattice QCD as a video game

The speed, bandwidth and cost characteristics of today's PC graphics cards make them an attractive target as general purpose computational platforms. High performance can be achieved also for lattice simulations but the actual implementation can be cumbersome. This paper outlines the architecture and programming model of modern graphics cards for the lattice practitioner with the goal of exploiting these chips for Monte Carlo simulations. Sample code is also given. (c) 2007 Elsevier B.V. All rights reserved

Enumerating transformation semigroups

This work was partially supported by the NeCTAR Research Cloud, an initiative of the Australian Government’s Super Science scheme and the Education Investment Fund; and by the EU Project BIOMICS (Contract Number CNECT-ICT-318202).We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation semigroups up to degree 4. Classification of these semigroups up to conjugacy, isomorphism and anti-isomorphism, by size and rank, provides a solid base for further investigations of transformation semigroups.PostprintPeer reviewe

Absorption and wavepackets in optically excited semiconductor superlattices driven by dc-ac fields

Within the one-dimensional tight-binding minibands and on-site Coloumbic interaction approximation, the absorption spectrum and coherent wavepacket time evolution in an optically excited semiconductor superlattice driven by dc-ac electric fields are investigated using the semiconductor Bloch equations. The dominating roles of the ratios of dc-Stark to external ac frequency, as well as ac-Stark to external ac frequency, is emphasized. If the former is an integer ${\cal N}$, then also ${\cal N}$ harmonics are present within one Stark frequency, while the fractional case leads to the formation of excitonic fractional ladders. The later ratio determines the size and profile of the wavepacket. In the absence of excitonic interaction it controls the maximum size wavepackets reach within one cycle, while the interaction produces a strong anisotropy and tends to palliate the dynamic wavepacket localization.Comment: 14 pages, 7 postscript figure