709 research outputs found
A parity breaking Ising chain Hamiltonian as a Brownian motor
We consider the translationally invariant but parity (left-right symmetry)
breaking Ising chain Hamiltonian \begin{equation} {\cal H} = -U_2\sum_{k}
s_{k}s_{k+1} - U_3\sum_{k} s_{k}s_{k+1}s_{k+3} \nonumber \end{equation} and let
this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations
show that perturbations forcing this system off equilibrium make it act as a
Brownian molecular motor which, in the lattice gas interpretation, transports
particles along the chain. We determine the particle current under various
different circumstances, in particular as a function of the ratio and
of the conserved magnetization . The symmetry of the term
in the Hamiltonian is discussedComment: 11 pages, 4 figure
The two-dimensional two-component plasma plus background on a sphere : Exact results
An exact solution is given for a two-dimensional model of a Coulomb gas, more
general than the previously solved ones. The system is made of a uniformly
charged background, positive particles, and negative particles, on the surface
of a sphere. At the special value of the reduced inverse
temperature, the classical equilibrium statistical mechanics is worked out~:
the correlations and the grand potential are calculated. The thermodynamic
limit is taken, and as it is approached the grand potential exhibits a
finite-size correction of the expected universal form.Comment: 23 pages, Plain Te
Charge renormalization and other exact coupling corrections in the dipolar effective interaction in an electrolyte near a dielectric wall
The aim of the paper is to study the renormalizations of the charge and of
the screening length that appear in the large-distance behavior of the
effective pairwise interaction between two charges in a dilute electrolyte
solution, both along a dielectric wall and in the bulk. The electrolyte is
described by the primitive model in the framework of classical statistical
mechanics and the electrostatic response of the wall is characterized by its
dielectric constant.Comment: 60 pages 9 figure
Granular Rough Sphere in a Low-Density Thermal Bath
We study the stationary state of a rough granular sphere immersed in a
thermal bath composed of point particles. When the center of mass of the sphere
is fixed the stationary angular velocity distribution is shown to be Gaussian
with an effective temperature lower than that of the bath. For a freely moving
rough sphere coupled to the thermostat via inelastic collisions we find a
condition under which the joint distribution of the translational and
rotational velocities is a product of Gaussian distributions with the same
effective temperature. In this rather unexpected case we derive a formula for
the stationary energy flow from the thermostat to the sphere in accordance with
Fourier law
New duality relation for the Discrete Gaussian SOS model on a torus
We construct a new duality for two-dimensional Discrete Gaussian models. It
is based on a known one-dimensional duality and on a mapping, implied by the
Chinese remainder theorem, between the sites of an torus and those
of a ring of sites. The duality holds for an arbitrary translation
invariant interaction potential between the height variables on
the torus. It leads to pairs of mutually dual potentials
and to a temperature inversion according to .
When is isotropic, duality renders an anisotropic
. This is the case, in particular, for the potential that is
dual to an isotropic nearest-neighbor potential. In the thermodynamic limit
this dual potential is shown to decay with distance according to an inverse
square law with a quadrupolar angular dependence. There is a single pair of
self-dual potentials . At the self-dual
temperature the height-height
correlation can be calculated explicitly; it is anisotropic and diverges
logarithmically with distance.Comment: 26 pages, 2 figure
The Ideal Conductor Limit
This paper compares two methods of statistical mechanics used to study a
classical Coulomb system S near an ideal conductor C. The first method consists
in neglecting the thermal fluctuations in the conductor C and constrains the
electric potential to be constant on it. In the second method the conductor C
is considered as a conducting Coulomb system the charge correlation length of
which goes to zero. It has been noticed in the past, in particular cases, that
the two methods yield the same results for the particle densities and
correlations in S. It is shown that this is true in general for the quantities
which depend only on the degrees of freedom of S, but that some other
quantities, especially the electric potential correlations and the stress
tensor, are different in the two approaches. In spite of this the two methods
give the same electric forces exerted on S.Comment: 19 pages, plain TeX. Submited to J. Phys. A: Math. Ge
Casimir force between two ideal-conductor walls revisited
The high-temperature aspects of the Casimir force between two neutral
conducting walls are studied. The mathematical model of "inert" ideal-conductor
walls, considered in the original formulations of the Casimir effect, is based
on the universal properties of the electromagnetic radiation in the vacuum
between the conductors, with zero boundary conditions for the tangential
components of the electric field on the walls. This formulation seems to be in
agreement with experiments on metallic conductors at room temperature. At high
temperatures or large distances, at least, fluctuations of the electric field
are present in the bulk and at the surface of a particle system forming the
walls, even in the high-density limit: "living" ideal conductors. This makes
the enforcement of the inert boundary conditions inadequate. Within a hierarchy
of length scales, the high-temperature Casimir force is shown to be entirely
determined by the thermal fluctuations in the conducting walls, modelled
microscopically by classical Coulomb fluids in the Debye-H\"{u}ckel regime. The
semi-classical regime, in the framework of quantum electrodynamics, is studied
in the companion letter by P.R.Buenzli and Ph.A.Martin, cond-mat/0506363,
Europhys.Lett.72, 42 (2005).Comment: 7 pages.One reference updated. Domain of validity of eq.(11)
correcte
Statistical properties of charged interfaces
We consider the equilibrium statistical properties of interfaces submitted to
competing interactions; a long-range repulsive Coulomb interaction inherent to
the charged interface and a short-range, anisotropic, attractive one due to
either elasticity or confinement. We focus on one-dimensional interfaces such
as strings. Model systems considered for applications are mainly aggregates of
solitons in polyacetylene and other charge density wave systems, domain lines
in uniaxial ferroelectrics and the stripe phase of oxides. At zero temperature,
we find a shape instability which lead, via phase transitions, to tilted
phases. Depending on the regime, elastic or confinement, the order of the
zero-temperature transition changes. Thermal fluctuations lead to a pure
Coulomb roughening of the string, in addition to the usual one, and to the
presence of angular kinks. We suggest that such instabilities might explain the
tilting of stripes in cuprate oxides. The 3D problem of the charged wall is
also analyzed. The latter experiences instabilities towards various tilted
phases separated by a tricritical point in the elastic regime. In the
confinement regime, the increase of dimensionality favors either the melting of
the wall into a Wigner crystal of its constituent charges or a strongly
inclined wall which might have been observed in nickelate oxides.Comment: 17 pages, 11 figure
Self-consistent equation for an interacting Bose gas
We consider interacting Bose gas in thermal equilibrium assuming a positive
and bounded pair potential such that 0<\int d\br V(r) = a<\infty.
Expressing the partition function by the Feynman-Kac functional integral yields
a classical-like polymer representation of the quantum gas. With Mayer graph
summation techniques, we demonstrate the existence of a self-consistent
relation between the density and the
chemical potential , valid in the range of convergence of Mayer series.
The function is equal to the sum of all rooted multiply connected graphs.
Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in
the mean-field limit only tree diagrams contribute and function
reduces to the free gas density.
We also investigate how to extend the validity of the self-consistent
relation beyond the convergence radius of Mayer series (vicinity of
Bose-Einstein condensation) and study dominant corrections to mean field. At
lowest order, the form of function is shown to depend on single polymer
partition function for which we derive lower and upper bounds and on the
resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.
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