SU(2) potentials in quantum gravity

We present investigations of the potential between static charges from a simulation of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.Comment: 3 pages, contribution to Lattice 94 conference, uuencoded compressed postscript fil

Enhanced diffusion by reciprocal swimming

Purcell's scallop theorem states that swimmers deforming their shapes in a time-reversible manner ("reciprocal" motion) cannot swim. Using numerical simulations and theoretical calculations we show here that in a fluctuating environment, reciprocal swimmers undergo, on time scales larger than that of their rotational diffusion, diffusive dynamics with enhanced diffusivities, possibly by orders of magnitude, above normal translational diffusion. Reciprocal actuation does therefore lead to a significant advantage over non-motile behavior for small organisms such as marine bacteria

Autism genetics: searching for specificity and convergence.

Advances in genetics and genomics have improved our understanding of autism spectrum disorders. As many genes have been implicated, we look to points of convergence among these genes across biological systems to better understand and treat these disorders

On the energy momentum dispersion in the lattice regularization

For a free scalar boson field and for U(1) gauge theory finite volume (infrared) and other corrections to the energy-momentum dispersion in the lattice regularization are investigated calculating energy eigenstates from the fall off behavior of two-point correlation functions. For small lattices the squared dispersion energy defined by $E_{\rm dis}^2=E_{\vec{k}}^2-E_0^2-4\sum_{i=1}^{d-1}\sin(k_i/2)^2$ is in both cases negative ($d$ is the Euclidean space-time dimension and $E_{\vec{k}}$ the energy of momentum $\vec{k}$ eigenstates). Observation of $E_{\rm dis}^2=0$ has been an accepted method to demonstrate the existence of a massless photon ($E_0=0$) in 4D lattice gauge theory, which we supplement here by a study of its finite size corrections. A surprise from the lattice regularization of the free field is that infrared corrections do {\it not} eliminate a difference between the groundstate energy $E_0$ and the mass parameter $M$ of the free scalar lattice action. Instead, the relation $E_0=\cosh^{-1} (1+M^2/2)$ is derived independently of the spatial lattice size.Comment: 9 pages, 2 figures. Parts of the paper have been rewritten and expanded to clarify the result

Configuration Space for Random Walk Dynamics

Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a configuration to be sampled depends on a number of unusual quantities, which are explained in this paper. This has been overlooked in recent literature, where the method is advertised for the calculation of canonical expectation values. We illustrate these points for the $2d$ Ising model. In addition, we proof a previously conjectured equation which relates microcanonical expectation values to the spectral density.Comment: Various minor changes, appendix added, Fig. 2 droppe

Non-Perturbative U(1) Gauge Theory at Finite Temperature

For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on $N_{\tau} N_s^3$ lattices for $N_{\tau}$ fixed by extrapolating spatial volumes of size $N_s\le 18$ to $N_s\to\infty$. Within the numerical accuracy of the thus obtained fits we find for $N_{\tau}=4$, 5 and~6 second order critical exponents, which exhibit no obvious $N_{\tau}$ dependence. The exponents are consistent with 3d Gaussian values, but not with either first order transitions or the universality class of the 3d XY model. As the 3d Gaussian fixed point is known to be unstable, the scenario of a yet unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of the possible explanations.Comment: Extended version after referee reports. 6 pages, 6 figure

Small eigenvalues of large Hankel matrices:The indeterminate case

In this paper we characterise the indeterminate case by the eigenvalues of the Hankel matrices being bounded below by a strictly positive constant. An explicit lower bound is given in terms of the orthonormal polynomials and we find expresions for this lower bound in a number of indeterminate moment problems.Comment: 14 pages, 1 figur