On the Dynamics of Light Quarks in QCD

We describe recent results concerning the behavior of lattice QCD with light dynamical Wilson and Staggered quarks. We show that it is possible to reach regions of parameter space with light pions $m_\pi\approx 0.2/a$ using Wilson fermions. If the Hybrid Molecular Dynamics (HMD) algorithm is used with the same parameters it gives incorrect results. We also present preliminary results using a higher-order integration scheme.Comment: 4 pages (all in postscript), proceedings of LAT'9

On the GI/M/1/N queue with multiple working vacations—analytic analysis and computation

AbstractWe consider finite buffer single server GI/M/1 queue with exhaustive service discipline and multiple working vacations. Service times during a service period, service times during a vacation period and vacation times are exponentially distributed random variables. System size distributions at pre-arrival and arbitrary epoch with some important performance measures such as, probability of blocking, mean waiting time in the system etc. have been obtained. The model has potential application in the area of communication network, computer systems etc. where a single channel is allotted for more than one source

Instabilities and Non-Reversibility of Molecular Dynamics Trajectories

The theoretical justification of the Hybrid Monte Carlo algorithm depends upon the molecular dynamics trajectories within it being exactly reversible. If computations were carried out with exact arithmetic then it would be easy to ensure such reversibility, but the use of approximate floating point arithmetic inevitably introduces violations of reversibility. In the absence of evidence to the contrary, we are usually prepared to accept that such rounding errors can be made small enough to be innocuous, but in certain circumstances they are exponentially amplified and lead to blatantly erroneous results. We show that there are two types of instability of the molecular dynamics trajectories which lead to this behavior, instabilities due to insufficiently accurate numerical integration of Hamilton's equations, and intrinsic chaos in the underlying continuous fictitious time equations of motion themselves. We analyze the former for free field theory, and show that it is essentially a finite volume effect. For the latter we propose a hypothesis as to how the Liapunov exponent describing the chaotic behavior of the fictitious time equations of motion for an asymptotically free quantum field theory behaves as the system is taken to its continuum limit, and explain why this means that instabilities in molecular dynamics trajectories are not a significant problem for Hybrid Monte Carlo computations. We present data for pure $SU(3)$ gauge theory and for QCD with dynamical fermions on small lattices to illustrate and confirm some of our results.Comment: 28 pages latex with 19 color postscript figures included by eps

Cost of the Generalised Hybrid Monte Carlo Algorithm for Free Field Theory

We study analytically the computational cost of the Generalised Hybrid Monte Carlo (GHMC) algorithm for free field theory. We calculate the Metropolis acceptance probability for leapfrog and higher-order discretisations of the Molecular Dynamics (MD) equations of motion. We show how to calculate autocorrelation functions of arbitrary polynomial operators, and use these to optimise the GHMC momentum mixing angle, the trajectory length, and the integration stepsize for the special cases of linear and quadratic operators. We show that long trajectories are optimal for GHMC, and that standard HMC is more efficient than algorithms based on Second Order Langevin Monte Carlo (L2MC), sometimes known as Kramers Equation. We show that contrary to naive expectations HMC and L2MC have the same volume dependence, but their dynamical critical exponents are z = 1 and z = 3/2 respectively.Comment: 54 pages, 3 figure

Progress in Lattice Field Theory Algorithms

I present a summary of recent algorithmic developments for lattice field theories. In particular I give a pedagogical introduction to the new Multicanonical algorithm, and discuss the relation between the Hybrid Overrelaxation and Hybrid Monte Carlo algorithms. I also attempt to clarify the role of the dynamical critical exponent z and its connection with `computational cost.' [Includes four PostScript figures]Comment: 27 page

The LHMC Algorithm for Free Field Theory: Reexamining Overrelaxation

We analyze the autocorrelations for the LHMC algorithm in the context of free field theory. In this case this is just Adler's overrelaxation algorithm. We consider the algorithm with even/odd, lexicographic, and random updates, and show that its efficiency depends crucially on this ordering of sites when optimized for a given class of operators. In particular, we show that, contrary to previous expectations, it is possible to eliminate critical slowing down (z[int]=0) for a class of interesting observables, including the magnetic susceptibility: this can be done with lexicographic updates but is not possible with even/odd (z[int]=1) or random (z[int]=2) updates. We are considering the dynamical critical exponent z[int] for integrated autocorrelations rather than for the exponential autocorrelation time; this is reasonable because it is the integrated autocorrelation which determines the cost of a Monte Carlo computation.Comment: LaTeX, 33 pages, 3 postscript figure

Single parameter scaling in 1-D localized absorbing systems

Numerical study of the scaling of transmission fluctuations in the 1-D localization problem in the presence of absorption is carried out. Violations of single parameter scaling for lossy systems are found and explained on the basis of a new criterion for different types of scaling behavior derived by Deych et al [Phys. Rev. Lett., {\bf 84}, 2678 (2000)].Comment: 7 pages, 6 figures, RevTex, submitted to Phys. Rev.

Rapidity distribution as a probe for elliptical flow at intermediate energies

Interplay between the spectator and participant matter in heavy-ion collisions is investigated within isospin dependent quantum molecular dynamics (IQMD) model in term of rapidity distribution of light charged particles. The effect of different types and size rapidity distributions is studied in elliptical flow. The elliptical flow patterns show important role of the nearby spectator matter on the participant zone. This role is further explained on the basis of passing time of the spectator and expansion time of the participant zone. The transition from the in-plane to out-of-plane is observed only when the mid-rapidity region is included in the rapidity bin, otherwise no transition occurs. The transition energy is found to be highly sensitive towards the size of the rapidity bin, while weakly on the type of the rapidity distribution. The theoretical results are also compared with the experimental findings and are found in good agreement.Comment: 8 figure

Hydrodynamics of domain growth in nematic liquid crystals

We study the growth of aligned domains in nematic liquid crystals. Results are obtained solving the Beris-Edwards equations of motion using the lattice Boltzmann approach. Spatial anisotropy in the domain growth is shown to be a consequence of the flow induced by the changing order parameter field (backflow). The generalization of the results to the growth of a cylindrical domain, which involves the dynamics of a defect ring, is discussed.Comment: 12 revtex-style pages, including 12 figures; small changes before publicatio

Anomalous density of states in a metallic film in proximity with a superconductor

We investigated the local electronic density of states in superconductor-normal metal (Nb-Au) bilayers using a very low temperature (60 mK) STM. High resolution tunneling spectra measured on the normal metal (Au) surface show a clear proximity effect with an energy gap of reduced amplitude compared to the bulk superconductor (Nb) gap. Within this mini-gap, the density of states does not reach zero and shows clear sub-gap features. We show that the experimental spectra cannot be described with the well-established Usadel equations from the quasi-classical theory.Comment: 4 pages, 5 figure