Low-Temperature Long-Time Simulations of Ising Ferromagnets using the Monte Carlo with Absorbing Markov Chains method

The Monte Carlo with Absorbing Markov Chains (MCAMC) method is introduced. This method is a generalization of the rejection-free method known as the $n$-fold way. The MCAMC algorithm is applied to the study of the very low-temperature properties of the lifetime of the metastable state of Ising ferromagnets. This is done both for square-lattice and cubic-lattice nearest-neighbor models. Comparison is made with exact low-temperature predictions, in particular the low-temperature predictions that the metastable lifetime is discontinuous at particular values of the field. This discontinuity for the square lattice is not seen in finite-temperatures studies. For the cubic lattice, it is shown that these `exact predictions' are incorrect near the fields where there are discontinuities. The low-temperature formula must be modified and the corrected low-temperature predictions are not discontinuous in the energy of the nucleating droplet.Comment: Submitted to Computer Physics Communicatinos, for proceedings of the Conference CCP2001, 4 figure

Electrical excitation of surface plasmons

We exploit a plasmon mediated two-step momentum downconversion scheme to convert low-energy tunneling electrons into propagating photons. Surface plasmon polaritons (SPPs) propagating along an extended gold nanowire are excited on one end by low-energy electron tunneling and are then converted to free-propagating photons at the other end. The separation of excitation and outcoupling proofs that tunneling electrons excite gap plasmons that subsequently couple to propagating plasmons. Our work shows that electron tunneling provides a non-optical, voltage-controlled and low-energy pathway for launching SPPs in nanostructures, such as plasmonic waveguide

Advanced Dynamic Algorithms for the Decay of Metastable Phases in Discrete Spin Models: Bridging Disparate Time Scales

An overview of advanced dynamical algorithms capable of spanning the widely disparate time scales that govern the decay of metastable phases in discrete spin models is presented. The algorithms discussed include constrained transfer-matrix, Monte Carlo with Absorbing Markov Chains (MCAMC), and projective dynamics (PD) methods. The strengths and weaknesses of each of these algorithms are discussed, with particular emphasis on identifying the parameter regimes (system size, temperature, and field) in which each algorithm works best.Comment: 12 pages, 4 figures, proceedings of the US-Japan bilateral seminar on `Understanding and Conquering Long Time Scales in Computer Simulations', July 1999, to appear in Int. J. Mod. Phys.

A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces

Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that preserve the dynamics of the model are described. These include the $n$-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC) algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use of these algorithms, they are applied to some simplified models of dynamic physical systems. The models studied include a model for ion motion through a pore such as a biological ion channel and the metastable decay of the ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic algorithms, which are in the class of parallel discrete event simulations, are discussed. Efforts are made to keep the article at an elementary level by concentrating on a simple model in each case that illustrates the use of the advanced dynamic Monte Carlo algorithm.Comment: 53 pages, 17 figure

Constraints on low energy QCD parameters from η→3π\eta \to 3\pi and ππ\pi\pi scattering

The $\eta \to 3\pi$ decays are a valuable source of information on low energy QCD. Yet they were not used for an extraction of the three flavor chiral symmetry breaking order parameters until now. We use a Bayesian approach in the framework of resummed chiral perturbation theory to obtain constraints on the quark condensate and pseudoscalar decay constant in the chiral limit. We compare our results with recent CHPT and lattice QCD fits and find some tension, as the $\eta \to 3\pi$ data seem to prefer a larger ratio of the chiral order parameters. The results also disfavor a very large value of the pseudoscalar decay constant in the chiral limit, which was found by some recent works. In addition, we present results of a combined analysis including $\eta \to 3\pi$ decays and $\pi\pi$ scattering and though the picture does not changed appreciably, we find some tension between the data we use. We also try to extract information on the mass difference of the light quarks, but the uncertainties prove to be large.Comment: 23 pages, 8 figure

Scale interactions in compressible rotating fluids

We study a triple singular limit for the scaled barotropic Navier-Stokes system modeling the motion of a rotating, compressible, and viscous fluid, where the Mach and Rossby numbers are proportional to a small parameter, while the Reynolds number becomes infinite. If the fluid is confined to an infinite slab bounded above and below by two parallel planes, the limit behavior is identified as a purely horizontal motion of an incompressible inviscid fluid, the evolution of which is described by an analogue of the Euler system