Can a flavour-conserving treatment improve things ?

In this work I would like to present some ideas on how to improve on the gauge sector in our lattice simulations at finite baryon density. The long standing problem, that we obtain an onset in thermodynamic quantities at a much smaller chemical potential than expected, could be related to an unphysical proliferation of flavours due to hard gluons close to the Brillouin edges. These hard gluons produce flavour non-conserving vertices to the fermion sector. They also produce excessive number of small instantons due to lattice dislocations. Both unphysical effects could increase the propagation in (di)-quarks to give the early onset in $\mu$. Thus we will present here a modified action that avoids large fields close to the lattice cutoff. Some of these ideas have been tested for SU(2) and are being implemented for SU(3).Comment: Talk presented at the Intl. Workshop on QCD at Finite Baryon Density in Bielefeld, April 98. 5 pp in Latex, uses espcrc1.st

Real time correlations at finite Temperature for the Ising model

After having developed a method that measures real time evolution of quantum systems at a finite temperature, we present here the simplest field theory where this scheme can be applied to, namely the 1+1 Ising model. We will compute the probability that if a given spin is up, some other spin will be up after a time $t$, the whole system being at temperature $T$. We can thus study spatial correlations and relaxation times at finite $T$. The fixed points that enable the continuum real time limit can be easily found for this model. The ultimate aim is to get to understand real time evolution in more complicated field theories, with quantum effects such as tunneling at finite temperature.Comment: 3 pp in Latex, 2 ps Figs., presented at the Latt98 Conf. in Boulder C

Finite Density Results for Wilson Fermions Using the Volume Method

Nonzero chemical potential studies with Wilson fermions should avoid the proliferation of flavor-equivalent nucleon states encountered with staggered formulation of fermions. However, conventional wisdom has been that finite baryon density calculations with Wilson fermions will be prohibitively expensive. We demonstrate that the volume method applied to Wilson fermions gives surprisingly stable results on a small number of configurations. It is pointed out that this method may be applied to any local or nonlocal gauge invariant quantity. Some illustrative results for $$and$$ at various values of $\mu$ in a quenched lattice simulation are given.Comment: 3pp, Dec. 94

Time evolution for quantum systems at finite temperature

This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation is non-perturbative and fully quantized. Various numerical methods used to compute the needed path integrals in complex time were tested and their effectiveness was compared. For checking the formalism we used the harmonic oscillator where the numerical results could be compared with exact solutions. Interesting results were also obtained for a system that presents tunneling. A ring of coupled oscillators was treated in order to try to check selfconsistency in the thermodynamic limit. The short time distribution seems to propagate causally in the relativistic case. Our formalism can be extended easily to field theories where it remains to be seen if relevant models will be computable.Comment: uuencoded, 14 pp in Latex, 8 ps Fig

Negative-Energy Spinors and the Fock Space of Lattice Fermions at Finite Chemical Potential

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial ``energy'' in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.Comment: 14p

Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-Ford

A \emph{metric tree embedding} of expected \emph{stretch~$\alpha \geq 1$} maps a weighted $n$-node graph $G = (V, E, \omega)$ to a weighted tree $T = (V_T, E_T, \omega_T)$ with $V \subseteq V_T$ such that, for all $v,w \in V$, $\operatorname{dist}(v, w, G) \leq \operatorname{dist}(v, w, T)$ and $operatorname{E}[\operatorname{dist}(v, w, T)] \leq \alpha \operatorname{dist}(v, w, G)$. Such embeddings are highly useful for designing fast approximation algorithms, as many hard problems are easy to solve on tree instances. However, to date the best parallel $(\operatorname{polylog} n)$-depth algorithm that achieves an asymptotically optimal expected stretch of $\alpha \in \operatorname{O}(\log n)$ requires $\operatorname{\Omega}(n^2)$ work and a metric as input. In this paper, we show how to achieve the same guarantees using $\operatorname{polylog} n$ depth and $\operatorname{\tilde{O}}(m^{1+\epsilon})$ work, where $m = |E|$ and $\epsilon > 0$ is an arbitrarily small constant. Moreover, one may further reduce the work to $\operatorname{\tilde{O}}(m + n^{1+\epsilon})$ at the expense of increasing the expected stretch to $\operatorname{O}(\epsilon^{-1} \log n)$. Our main tool in deriving these parallel algorithms is an algebraic characterization of a generalization of the classic Moore-Bellman-Ford algorithm. We consider this framework, which subsumes a variety of previous "Moore-Bellman-Ford-like" algorithms, to be of independent interest and discuss it in depth. In our tree embedding algorithm, we leverage it for providing efficient query access to an approximate metric that allows sampling the tree using $\operatorname{polylog} n$ depth and $\operatorname{\tilde{O}}(m)$ work. We illustrate the generality and versatility of our techniques by various examples and a number of additional results

Extended instantons generated on the lattice

We have been able to observe directly extended instantons on the lattice, with a new method that does not require dislocations to measure them, and where we do not perform cooling. We showed, based on the simple Abelian Higgs model in $1+1$ dim., that one can extract the instanton and anti-instanton density and their size, by measuring the topological charge, $Q_v$ , on sub-volumes $v$ larger than the instanton sizes, but smaller than the periodic lattice of size $V$. We are working on the generalization for non-abelian models.Comment: Talk presented at the LATTICE96(topology) ,uuencoded 3 pp in Latex, 1 ps fig., uses espcrc2.sty and epsf to include fi

Homologous and unique G protein alpha subunits in the nematode Caenorhabditis elegans

A cDNA corresponding to a known G protein alpha subunit, the alpha subunit of Go (Go alpha), was isolated and sequenced. The predicted amino acid sequence of C. elegans Go alpha is 80-87% identical to other Go alpha sequences. An mRNA that hybridizes to the C. elegans Go alpha cDNA can be detected on Northern blots. A C. elegans protein that crossreacts with antibovine Go alpha antibody can be detected on immunoblots. A cosmid clone containing the C. elegans Go alpha gene (goa-1) was isolated and mapped to chromosome I. The genomic fragments of three other C. elegans G protein alpha subunit genes (gpa-1, gpa-2, and gpa-3) have been isolated using the polymerase chain reaction. The corresponding cosmid clones were isolated and mapped to disperse locations on chromosome V. The sequences of two of the genes, gpa-1 and gpa-3, were determined. The predicted amino acid sequences of gpa-1 and gpa-3 are only 48% identical to each other. Therefore, they are likely to have distinct functions. In addition they are not homologous enough to G protein alpha subunits in other organisms to be classified. Thus C. elegans has G proteins that are identifiable homologues of mammalian G proteins as well as G proteins that appear to be unique to C. elegans. Study of identifiable G proteins in C. elegans may result in a further understanding of their function in other organisms, whereas study of the novel G proteins may provide an understanding of unique aspects of nematode physiology