192 research outputs found
Local Simulation Algorithms for Coulomb Gases with Dynamical Dielectric Effects
We discuss the application of the local lattice technique of Maggs and
Rossetto to problems that involve the motion of objects with different
dielectric constants than the background. In these systems the simulation
method produces a spurious interaction force which causes the particles to move
in an unphysical manner. We show that this term can be removed using a variant
of a method known from high-energy physics simulations, the multiboson method,
and demonstrate the effectiveness of this corrective method on a system of
neutral particles. We then apply our method to a one-component plasma to show
the effect of the spurious interaction term on a charged system.Comment: 13 pages, 4 figure
On the reliability of mean-field methods in polymer statistical mechanics
The reliability of the mean-field approach to polymer statistical mechanics
is investigated by comparing results from a recently developed lattice
mean-field theory (LMFT) method to statistically exact results from two
independent numerical Monte Carlo simulations for the problems of a polymer
chain moving in a spherical cavity and a polymer chain partitioning between two
confining spheres of different radii. It is shown that in some cases the
agreement between the LMFT and the simulation results is excellent, while in
others, such as the case of strongly fluctuating monomer repulsion fields, the
LMFT results agree with the simulations only qualitatively. Various
approximations of the LMFT method are systematically estimated, and the
quantitative discrepancy between the two sets of results is explained with the
diminished accuracy of the saddle-point approximation, implicit in the
mean-field method, in the case of strongly fluctuating fields.Comment: 27 pages, 9 figure
Toward a Monte Carlo Theory of Quantum Dynamics
We consider in the present paper an extension of numerical path integral methods for use in computing finite temperature time correlation functions. We demonstrate that coordinate rotation techniques extend appreciably the time domain over which Monte Carlo methods are of use in the construction of such correlation functions
The osmotic pressure of charged colloidal suspensions: A unified approach to linearized Poisson-Boltzmann theory
We study theoretically the osmotic pressure of a suspension of charged
objects (e.g., colloids, polyelectrolytes, clay platelets, etc.) dialyzed
against an electrolyte solution using the cell model and linear
Poisson-Boltzmann (PB) theory. From the volume derivative of the grand
potential functional of linear theory we obtain two novel expressions for the
osmotic pressure in terms of the potential- or ion-profiles, neither of which
coincides with the expression known from nonlinear PB theory, namely, the
density of microions at the cell boundary. We show that the range of validity
of linearization depends strongly on the linearization point and proof that
expansion about the selfconsistently determined average potential is optimal in
several respects. For instance, screening inside the suspension is
automatically described by the actual ionic strength, resulting in the correct
asymptotics at high colloid concentration. Together with the analytical
solution of the linear PB equation for cell models of arbitrary dimension and
electrolyte composition explicit and very general formulas for the osmotic
pressure ensue. A comparison with nonlinear PB theory is provided. Our analysis
also shows that whether or not linear theory predicts a phase separation
depends crucially on the precise definition of the pressure, showing that an
improper choice could predict an artificial phase separation in systems as
important as DNA in physiological salt solution.Comment: 16 pages, 5 figures, REVTeX4 styl
The `Friction' of Vacuum, and other Fluctuation-Induced Forces
The static Casimir effect describes an attractive force between two
conducting plates, due to quantum fluctuations of the electromagnetic (EM)
field in the intervening space. {\it Thermal fluctuations} of correlated fluids
(such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are
also modified by the boundaries, resulting in finite-size corrections at
criticality, and additional forces that effect wetting and layering phenomena.
Modified fluctuations of the EM field can also account for the `van der Waals'
interaction between conducting spheres, and have analogs in the
fluctuation--induced interactions between inclusions on a membrane. We employ a
path integral formalism to study these phenomena for boundaries of arbitrary
shape. This allows us to examine the many unexpected phenomena of the dynamic
Casimir effect due to moving boundaries. With the inclusion of quantum
fluctuations, the EM vacuum behaves essentially as a complex fluid, and
modifies the motion of objects through it. In particular, from the mechanical
response function of the EM vacuum, we extract a plethora of interesting
results, the most notable being: (i) The effective mass of a plate depends on
its shape, and becomes anisotropic. (ii) There is dissipation and damping of
the motion, again dependent upon shape and direction of motion, due to emission
of photons. (iii) There is a continuous spectrum of resonant cavity modes that
can be excited by the motion of the (neutral) boundaries.Comment: RevTex, 2 ps figures included. The presentation is completely
revised, and new sections are adde
Displaced squeezed number states: Position space representation, inner product, and some applications
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