1,335 research outputs found
A Lattice Gas Coupled to Two Thermal Reservoirs: Monte Carlo and Field Theoretic Studies
We investigate the collective behavior of an Ising lattice gas, driven to
non-equilibrium steady states by being coupled to {\em two} thermal baths.
Monte Carlo methods are applied to a two-dimensional system in which one of the
baths is fixed at infinite temperature. Both generic long range correlations in
the disordered state and critical poperties near the second order transition
are measured. Anisotropic scaling, a key feature near criticality, is used to
extract and some critical exponents. On the theoretical front, a
continuum theory, in the spirit of Landau-Ginzburg, is presented. Being a
renormalizable theory, its predictions can be computed by standard methods of
-expansions and found to be consistent with simulation data. In
particular, the critical behavior of this system belongs to a universality
class which is quite {\em different} from the uniformly driven Ising model.Comment: 21 pages, 15 figure
Getting More from Pushing Less: Negative Specific Heat and Conductivity in Non-equilibrium Steady States
For students familiar with equilibrium statistical mechanics, the notion of a
positive specific heat, being intimately related to the idea of stability, is
both intuitively reasonable and mathematically provable. However, for system in
non-equilibrium stationary states, coupled to more than one energy reservoir
(e.g., thermal bath), negative specific heat is entirely possible. In this
paper, we present a ``minimal'' system displaying this phenomenon. Being in
contact with two thermal baths at different temperatures, the (internal) energy
of this system may increase when a thermostat is turned down. In another
context, a similar phenomenon is negative conductivity, where a current may
increase by decreasing the drive (e.g., an external electric field). The
counter-intuitive behavior in both processes may be described as `` getting
more from pushing less.'' The crucial ingredients for this phenomenon and the
elements needed for a ``minimal'' system are also presented.Comment: 14 pages, 3 figures, accepted for publication in American Journal of
Physic
Contrasts between Equilibrium and Non-equilibrium Steady States: Computer Aided Discoveries in Simple Lattice Gases
A century ago, the foundations of equilibrium statistical mechanics were
laid. For a system in equilibrium with a thermal bath, much is understood
through the Boltzmann factor, exp{-H[C]/kT}, for the probability of finding the
system in any microscopic configuration C. In contrast, apart from some special
cases, little is known about the corresponding probabilities, if the same
system is in contact with more than one reservoir of energy, so that, even in
stationary states, there is a constant energy flux through our system. These
non-equilibrium steady states display many surprising properties. In
particular, even the simplest generalization of the Ising model offers a wealth
of unexpected phenomena. Mostly discovered through Monte Carlo simulations,
some of the novel properties are understood while many remain unexplained. A
brief review and some recent results will be presented, highlighting the sharp
contrasts between the equilibrium Ising system and this non-equilibrium
counterpart.Comment: 9 pages, 3 figure
Roughening transition, surface tension and equilibrium droplet shapes in a two-dimensional Ising system
The exact surface tension for all angles and temperatures is given for the two-dimensional square Ising system with anisotropic nearest-neighbour interactions. Using this in the Wulff construction, droplet shapes are computed and illustrated. Letting temperature approach zero allows explicit study of the roughening transition in this model. Results are compared with those of the solid-on-solid approximation
Factorised Steady States in Mass Transport Models on an Arbitrary Graph
We study a general mass transport model on an arbitrary graph consisting of
nodes each carrying a continuous mass. The graph also has a set of directed
links between pairs of nodes through which a stochastic portion of mass, chosen
from a site-dependent distribution, is transported between the nodes at each
time step. The dynamics conserves the total mass and the system eventually
reaches a steady state. This general model includes as special cases various
previously studied models such as the Zero-range process and the Asymmetric
random average process. We derive a general condition on the stochastic mass
transport rules, valid for arbitrary graph and for both parallel and random
sequential dynamics, that is sufficient to guarantee that the steady state is
factorisable. We demonstrate how this condition can be achieved in several
examples. We show that our generalized result contains as a special case the
recent results derived by Greenblatt and Lebowitz for -dimensional
hypercubic lattices with random sequential dynamics.Comment: 17 pages 1 figur
Solving dielectric and plasmonic waveguide dispersion relations with a pocket calculator
We present a robust iterative technique for solving complex transcendental
dispersion equations routinely encountered in integrated optics. Our method
especially befits the multilayer dielectric and plasmonic waveguides forming
the basis structures for a host of contemporary nanophotonic devices. The
solution algorithm ports seamlessly from the real to the complex domain--i.e.,
no extra complexity results when dealing with leaky structures or those with
material/metal loss. Unlike several existing numerical approaches, our
algorithm exhibits markedly-reduced sensitivity to the initial guess and allows
for straightforward implementation on a pocket calculator.Comment: 18 pages, 11 Figures, 5 Tables, added references, Submitted to Optics
Expres
Driven Diffusive Systems: How Steady States Depend on Dynamics
In contrast to equilibrium systems, non-equilibrium steady states depend
explicitly on the underlying dynamics. Using Monte Carlo simulations with
Metropolis, Glauber and heat bath rates, we illustrate this expectation for an
Ising lattice gas, driven far from equilibrium by an `electric' field. While
heat bath and Glauber rates generate essentially identical data for structure
factors and two-point correlations, Metropolis rates give noticeably weaker
correlations, as if the `effective' temperature were higher in the latter case.
We also measure energy histograms and define a simple ratio which is exactly
known and closely related to the Boltzmann factor for the equilibrium case. For
the driven system, the ratio probes a thermodynamic derivative which is found
to be dependent on dynamics
Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process
As a solvable and broadly applicable model system, the totally asymmetric
exclusion process enjoys iconic status in the theory of non-equilibrium phase
transitions. Here, we focus on the time dependence of the total number of
particles on a 1-dimensional open lattice, and its power spectrum. Using both
Monte Carlo simulations and analytic methods, we explore its behavior in
different characteristic regimes. In the maximal current phase and on the
coexistence line (between high/low density phases), the power spectrum displays
algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the
high/low density phases, we find pronounced \emph{oscillations}, which damp
into power laws. This behavior can be understood in terms of driven biased
diffusion with conserved noise in the bulk.Comment: 4 pages, 4 figure
The Effects of Next-Nearest-Neighbor Interactions on the Orientation Dependence of Step Stiffness: Reconciling Theory with Experiment for Cu(001)
Within the solid-on-solid (SOS) approximation, we carry out a calculation of
the orientational dependence of the step stiffness on a square lattice with
nearest and next-nearest neighbor interactions. At low temperature our result
reduces to a simple, transparent expression. The effect of the strongest trio
(three-site, non pairwise) interaction can easily be incorporated by modifying
the interpretation of the two pairwise energies. The work is motivated by a
calculation based on nearest neighbors that underestimates the stiffness by a
factor of 4 in directions away from close-packed directions, and a subsequent
estimate of the stiffness in the two high-symmetry directions alone that
suggested that inclusion of next-nearest-neighbor attractions could fully
explain the discrepancy. As in these earlier papers, the discussion focuses on
Cu(001).Comment: 8 pages, 3 figures, submitted to Phys. Rev.
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