31,944 research outputs found
Fluctuation relations for equilibrium states with broken discrete or continuous symmetries
Isometric fluctuation relations are deduced for the fluctuations of the order
parameter in equilibrium systems of condensed-matter physics with broken
discrete or continuous symmetries. These relations are similar to their
analogues obtained for non-equilibrium systems where the broken symmetry is
time reversal. At equilibrium, these relations show that the ratio of the
probabilities of opposite fluctuations goes exponentially with the
symmetry-breaking external field and the magnitude of the fluctuations. These
relations are applied to the Curie-Weiss, Heisenberg, and ~models of
magnetism where the continuous rotational symmetry is broken, as well as to the
-state Potts model and the -state clock model where discrete symmetries
are broken. Broken symmetries are also considered in the anisotropic
Curie-Weiss model. For infinite systems, the results are calculated using
large-deviation theory. The relations are also applied to mean-field models of
nematic liquid crystals where the order parameter is tensorial. Moreover, their
extension to quantum systems is also deduced.Comment: 34 pages, 14 figure
Nonlinear transport effects in mass separation by effusion
Generalizations of Onsager reciprocity relations are established for the
nonlinear response coefficients of ballistic transport in the effusion of
gaseous mixtures. These generalizations, which have been established on the
basis of the fluctuation theorem for the currents, are here considered for mass
separation by effusion. In this kinetic process, the mean values of the
currents depend nonlinearly on the affinities or thermodynamic forces
controlling the nonequilibrium constraints. These nonlinear transport effects
are shown to play an important role in the process of mass separation. In
particular, the entropy efficiency turns out to be significantly larger than it
would be the case if the currents were supposed to depend linearly on the
affinities
Phase transition for continuum Widom-Rowlinson model with random radii
In this paper we study the phase transition of continuum Widom-Rowlinson
measures in with types of particles and random radii. Each
particle of type is marked by a random radius distributed by a
probability measure on . The particles of same type do not
interact each other whereas particles and with different type interact via an exclusion hardcore interaction forcing to be
smaller than . In the integrable case (i.e. , ), we show that the Widom-Rowlinson measures
exhibit a standard phase transition providing uniqueness, when the activity is
small, and co-existence of ordered phases, when the activity is large. In
the non-integrable case (i.e. , ), we
show another type of phase transition. We prove, when the activity is small,
the existence of at least extremal phases and we conjecture that, when
the activity is large, only the ordered phases subsist. We prove a weak
version of this conjecture by showing that the symmetric Widom-Rowlinson
measure with free boundary condition is a mixing of the ordered phases if
and only if the activity is large.Comment: 25 pages, 0 figur
Diffusion and Correlations in Lattice Gas Automata
We present an analysis of diffusion in terms of the spontaneous density
fluctuations in a non-thermal two-species fluid modeled by a lattice gas
automaton. The power spectrum of the density correlation function is computed
with statistical mechanical methods, analytically in the hydrodynamic limit,
and numerically from a Boltzmann expression for shorter time and space scales.
In particular we define an observable -- the weighted difference of the species
densities -- whose fluctuation correlations yield the diffusive mode
independently of the other modes so that the corresponding power spectrum
provides a measure of diffusion dynamics solely. Automaton simulations are
performed to obtain measurements of the spectral density over the complete
range of wavelengths (from the microscopic scale to the macroscopic scale of
the automaton universe). Comparison of the theoretical results with the
numerical experiments data yields the following results: (i) the spectral
functions of the lattice gas fluctuations are in accordance with those of a
classical `non-thermal' fluid; (ii) the Landau-Placzek theory, obtained as the
hydrodynamic limit of the Boltzmann theory, describes the spectra correctly in
the long wavelength limit; (iii) at shorter wavelengths and at moderate
densities the complete Boltzmann theory provides good agreement with the
simulation data. These results offer convincing validation of lattice gas
automata as a microscopic approach to diffusion phenomena in fluid systems.Comment: 9 pages (revtex source), 12 Postscript figure
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