690 research outputs found
Critical Point Field Mixing in an Asymmetric Lattice Gas Model
The field mixing that manifests broken particle-hole symmetry is studied for
a 2-D asymmetric lattice gas model having tunable field mixing properties.
Monte Carlo simulations within the grand canonical ensemble are used to obtain
the critical density distribution for different degrees of particle-hole
asymmetry. Except in the special case when this asymmetry vanishes, the density
distributions exhibit an antisymmetric correction to the limiting
scale-invariant form. The presence of this correction reflects the mixing of
the critical energy density into the ordering operator. Its functional form is
found to be in excellent agreement with that predicted by the mixed-field
finite-size-scaling theory of Bruce and Wilding. A computational procedure for
measuring the significant field mixing parameter is also described, and its
accuracy gauged by comparing the results with exact values obtained
analytically.Comment: 10 Pages, LaTeX + 8 figures available from author on request, To
appear in Z. Phys.
The ideal trefoil knot
The most tight conformation of the trefoil knot found by the SONO algorithm
is presented. Structure of the set of its self-contact points is analyzed.Comment: 11 pages, 8 figure
Fluid-membrane tethers: minimal surfaces and elastic boundary layers
Thin cylindrical tethers are common lipid bilayer membrane structures,
arising in situations ranging from micromanipulation experiments on artificial
vesicles to the dynamic structure of the Golgi apparatus. We study the shape
and formation of a tether in terms of the classical soap-film problem, which is
applied to the case of a membrane disk under tension subject to a point force.
A tether forms from the elastic boundary layer near the point of application of
the force, for sufficiently large displacement. Analytic results for various
aspects of the membrane shape are given.Comment: 12 page
Input-output theory for fermions in an atom cavity
We generalize the quantum optical input-output theory developed for optical
cavities to ultracold fermionic atoms confined in a trapping potential, which
forms an "atom cavity". In order to account for the Pauli exclusion principle,
quantum Langevin equations for all cavity modes are derived. The dissipative
part of these multi-mode Langevin equations includes a coupling between cavity
modes. We also derive a set of boundary conditions for the Fermi field that
relate the output fields to the input fields and the field radiated by the
cavity. Starting from a constant uniform current of fermions incident on one
side of the cavity, we use the boundary conditions to calculate the occupation
numbers and current density for the fermions that are reflected and transmitted
by the cavity
Slow fluctuations in enhanced Raman scattering and surface roughness relaxation
We propose an explanation for the recently measured slow fluctuations and
``blinking'' in the surface enhanced Raman scattering (SERS) spectrum of single
molecules adsorbed on a silver colloidal particle. We suggest that these
fluctuations may be related to the dynamic relaxation of the surface roughness
on the nanometer scale and show that there are two classes of roughness with
qualitatively different dynamics. The predictions agree with measurements of
surface roughness relaxation. Using a theoretical model for the kinetics of
surface roughness relaxation in the presence of charges and optical electrical
fields, we predict that the high-frequency electromagnetic field increases both
the effective surface tension and the surface diffusion constant and thus
accelerates the surface smoothing kinetics and time scale of the Raman
fluctuations in manner that is linear with the laser power intensity, while the
addition of salt retards the surface relaxation kinetics and increases the time
scale of the fluctuations. These predictions are in qualitative agreement with
the Raman experiments
Coherently Scattering Atoms from an Excited Bose-Einstein Condensate
We consider scattering atoms from a fully Bose-Einstein condensed gas. If we
take these atoms to be identical to those in the Bose-Einstein condensate, this
scattering process is to a large extent analogous to Andreev reflection from
the interface between a superconducting and a normal metal. We determine the
scattering wave function both in the absence and the presence of a vortex. Our
results show a qualitative difference between these two cases that can be
understood as due to an Aharonov-Bohm effect. It leads to the possibility to
experimentally detect and study vortices in this way.Comment: 5 pages of ReVTeX and 2 postscript figure
Fluctuating Elastic Rings: Statics and Dynamics
We study the effects of thermal fluctuations on elastic rings. Analytical
expressions are derived for correlation functions of Euler angles, mean square
distance between points on the ring contour, radius of gyration, and
probability distribution of writhe fluctuations. Since fluctuation amplitudes
diverge in the limit of vanishing twist rigidity, twist elasticity is essential
for the description of fluctuating rings. We find a crossover from a small
scale regime in which the filament behaves as a straight rod, to a large scale
regime in which spontaneous curvature is important and twist rigidity affects
the spatial configurations of the ring. The fluctuation-dissipation relation
between correlation functions of Euler angles and response functions, is used
to study the deformation of the ring by external forces. The effects of inertia
and dissipation on the relaxation of temporal correlations of writhe
fluctuations, are analyzed using Langevin dynamics.Comment: 43 pages, 9 Figure
Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators
We study domain growth in a nonlinear optical system useful to explore
different scenarios that might occur in systems which do not relax to
thermodynamic equilibrium. Domains correspond to equivalent states of different
circular polarization of light. We describe three dynamical regimes: a
coarsening regime in which dynamical scaling holds with a growth law dictated
by curvature effects, a regime in which localized structures form, and a regime
in which polarization domain walls are modulationally unstable and the system
freezes in a labyrinthine pattern.Comment: 13 pages, 6 figure
Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems
The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model
are studied using a phase dynamics approach. A Cross-Newell phase equation
describing slow and weak modulations of periodic stationary solutions is
derived. The derivation applies to the bistable, excitable, and the Turing
unstable regimes. In the bistable case stability thresholds are obtained for
the Eckhaus and the zigzag instabilities and for the transition to traveling
waves. Neutral stability curves demonstrate the destabilization of stationary
planar patterns at low wavenumbers to zigzag and traveling modes. Numerical
solutions of the model system support the theoretical findings
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