We show how to achieve lattice-spacing independent results
in numerical simulations of finite-temperature stochastic
scalar field theories. We generalize the previous approach
of one of us by obtaining results which are independent of
the renormalization scale. As an application of our method,
we examine thermal phase mixing in the context of
Ginzburg-Landau models with short-range interactions. In
particular, we obtain the lattice-spacing and
renormalization-scale independent critical value of the
control parameter which determines the free-energy barrier
between the two low-temperature phases. We also propose a
simple procedure to extract the critical value of control
parameters for different choices of lattice spacing.
[H4.002] Quantifying Non-Equilibrium Behavior with Varying Quench Rates
Carmen Gagne, Marcelo Gleiser (Dartmouth College)
We investigate nonequilibrium behavior in (1+1)-dimensional stochastic
field theories in the context of Ginzburg-Landau models at varying
cooling rates. We argue that a reliable measure of the departure
from thermal equilibrium can be obtained from the
absolute value of the rate of change of the momentum-integrated structure
function, \Delta S_T . We show that the peak of \Delta S_T
scales with the quenching time-scale, \tau _q , in agreement with
the prediction by Zurek et al. [PRD 58, 085021 (1998)] for both over and
under-damped regimes. Furthermore, we show that the amplitude of the
peak scales as \tau _q^-6 / 5 independent of the viscosity.
[H4.003] Disclination loop behavior near the nematic-isotropic phase transition
Nikolai Priezjev, Robert Pelcovits (Department of Physics, Brown University, Providence RI 02912)
We investigate the behavior of disclination loops in the
vicinity of the first order nematic-isotropic transition in
the Lebwohl-Lasher model using a cluster Monte Carlo
algorithm. We calculate the distribution function D(p) of
disclination loops of perimeter p for different temperatures
and fit it to a quasiexponential form. At the transition
temperature we find the power law exponent approximately
equal to 5/2, corresponding to random walk behavior in three
dimensions. We expect the disclination line tension to jump
discontinuously at the transition; however, the transition
is too weakly first order to allow measurement of the jump.
Instead we measure the jump in a modified model with a more
strongly first order transition. We also study the
composition of the loops in terms of wedge and twist line
segments.
[H4.004] Quantum tunneling double-barrier penetration and the substituent effect on non-linear I/V characteristics in a two-terminal molecular electronic device
Karl Sohlberg (Department of Chemistry, Drexel University), Nikita Matsunaga (Department of Chemistry and Biochemistry, Long Island University)
Recently there has been an explosion of interest in the
potential use of individual molecules as electronic device
elements. The electrical characteristics of molecular
junctions, individual molecules spanning the gap between two
metal electrodes, have been reported and certain molecular
species have been found to exhibit negative differential
resistance (NDR). We propose that NDR in molecular junctions
results from resonant tunneling. We present a quantum
mechanical tunneling model for the electron transport
through such a junction and dress the model with the results
of quantum chemical electronic structure calculations. The
proposed model not only gives insight into the origin of NDR
in molecular junctions, but explains the effect of
substituent functional groups on the junction molecule and
allows us to investigate the spatial variation of the
electrostatic potential across the junction.
[H4.005] Computing with Category Theory
Saul Youssef (Center for Computational Science, Boston University)
Although category theory is one of the most useful ideas in mathematics and although category theoretical ideas have penetrated much of mathematics, theoretical physics and other fields, these ideas have had little impact
on computational physics. I will discuss why computing with category theory is an interesting idea and describe the kernal of a math library organized around category theory and written in ``Aldor" -- a language developed by Stephen Watt and collaborators and currently under development at NAG.
[H4.006] A molecular-dynamics study of melting and orientational order of the screened Wigner crystal on helium films
José Pedro Rino, Paulo S. Branício, Nelson Studart (Departamento de Física - Universidade Federal de São Carlos, São Carlos, SP-BRAZIL)
Molecular-dynamics simulations were employed to study the
melting of two-dimensional electrons interacting via a
screened Coulomb potential, which describes the interaction
between surface electrons on a helium film. MD simulation
was performed for a system of N=3600 electrons in a
rectangular box for a fixed density of 1.3x10 ^-10 cm
^-2 which is the maximum attainable electron density.
All the results were obtained at constant temperature using
the NVT ensemble based on the Nosé-Hoover chain dynamics
to control appropriately the temperature. We apply periodic
boundary conditions and the Ewald summation to take care of
the long-range interaction. The dimensions of the MD cell
has a ratio of \sqrt3/2 in order to accommodate a
perfect triangular lattice with 4M^2 (M being an
integer) electrons. The equations of motion were integrated
using a velocity-Verlet algorithm with a corresponding time
step of \Delta t=10 ^-13 s, which conserves the energy
at least 1 part in 10^4, after several thousands time
steps run. The simulations were performed in series; i.e.,
the equilibrated configuration obtained for a given
temperature was used as input for another simulation in a
slightly higher or lower temperature. We calculated
orientational correlation functions to study the nature of
the phase transition by varying the screening parameters
from the pure Wigner crystal (electrons on bulk helium)
until the dipolar crystal (electrons trapped on a helium
film over a metal substrate). We studied also the formation
of defects in the system. Our results indicate no evidence
of the ''hexatic'' phase between the solid and liquid
phases.
[H4.007] Elucidating Mechanisms of Extensive Chaos
David A. Egolf (Dept. of Physics, Georgetown University and CNLS, Los Alamos National Laboratory), Ilarion V. Melnikov (Dept. of Physics, Duke University), Werner Pesch (Theoretical Physics II, University of Bayreuth), Robert E. Ecke (MST-10 and CNLS, Los Alamos National Laboratory)
We report studies of the mechanism for the generation of
chaotic disorder in a phenomenon found in nature,
Rayleigh-Bénard convection (RBC), in a regime exhaustively
studied experimentally. Through large-scale,
parallel-computational studies of the detailed space-time
evolution of the dynamical degrees of freedom, we find that
the Spiral Defect Chaos (SDC) state of RBC is spatially- and
temporally- localized to defect creation/annihilation events
(D.A. Egolf, I.V. Melnikov, W. Pesch, and R.E. Ecke, Nature,
404:733--736, 2000), and we elucidate how these divergent,
but very brief, events lead to eventual macroscopic
differences between initially similar flow patterns. We also
demonstrate that SDC is extensively chaotic, in that the
number of dynamical degrees of freedom (the fractal
dimension) is proportional to the system size, suggesting
the possibility for a hydrodynamic-like description of the
long-wavelength properties of SDC. The computational
technique employed shows promise for analyzing a wide
variety of extended dynamical systems.
[H4.008] Relationship between Potential Energy Landscapes and the Melting Transition
Charusita Chakravarty, Pooja Shah (Department of Chemistry, Indian Institute of Technology-Delhi, Hauz Khas, New Delhi 110016, India.)
Pair-additive Morse potentials are used to illustrate the effect of varying range and curvature of the pair interaction on the potential energy landscape and the melting transition. The potential energy landscape is analysed in terms of the configurational energies and normal mode properties of instantaneous, saddle and quenched configurations sampled from isothermal-isobaric ensemble simulations. Distinctive statistical features of the three categories of configurations in the liquid and solid phases, as well as changes in landscape properties on melting, are discussed. Comparisons are made with quantum and classical Lennard-Jones systems.