585 research outputs found
Comment on "Universal Fluctuations in Correlated Systems"
This is a Comment on "Universal Fluctuations in Correlated Systems".Comment: to appear in Phys. Rev. Let
Onsager's Wien Effect on a Lattice
The Second Wien Effect describes the non-linear, non-equilibrium response of
a weak electrolyte in moderate to high electric fields. Onsager's 1934
electrodiffusion theory along with various extensions has been invoked for
systems and phenomena as diverse as solar cells, surfactant solutions, water
splitting reactions, dielectric liquids, electrohydrodynamic flow, water and
ice physics, electrical double layers, non-Ohmic conduction in semiconductors
and oxide glasses, biochemical nerve response and magnetic monopoles in spin
ice. In view of this technological importance and the experimental ubiquity of
such phenomena, it is surprising that Onsager's Wien effect has never been
studied by numerical simulation. Here we present simulations of a lattice
Coulomb gas, treating the widely applicable case of a double equilibrium for
free charge generation. We obtain detailed characterisation of the Wien effect
and confirm the accuracy of the analytical theories as regards the field
evolution of the free charge density and correlations. We also demonstrate that
simulations can uncover further corrections, such as how the field-dependent
conductivity may be influenced by details of microscopic dynamics. We conclude
that lattice simulation offers a powerful means by which to investigate
system-specific corrections to the Onsager theory, and thus constitutes a
valuable tool for detailed theoretical studies of the numerous practical
applications of the Second Wien Effect.Comment: Main: 12 pages, 4 figures. Supplementary Information: 7 page
Universal Magnetic Fluctuations with a Field Induced Length Scale
We calculate the probability density function for the order parameter
fluctuations in the low temperature phase of the 2D-XY model of magnetism near
the line of critical points. A finite correlation length, \xi, is introduced
with a small magnetic field, h, and an accurate expression for \xi(h) is
developed by treating non-linear contributions to the field energy using a
Hartree approximation. We find analytically a series of universal non-Gaussian
distributions with a finite size scaling form and present a Gumbel-like
function that gives the PDF to an excellent approximation. We propose the
Gumbel exponent, a(h), as an indirect measure of the length scale of
correlations in a wide range of complex systems.Comment: 7 pages, 4 figures, 1 table. To appear in Phys. Rev.
Linearity and Scaling of a Statistical Model for the Species Abundance Distribution
We derive a linear recursion relation for the species abundance distribution
in a statistical model of ecology and demonstrate the existence of a scaling
solution
Dynamic susceptibility of a spin ice near the critical point
We consider spin ice magnets (primarily, ) in the
vicinity of their critical point on the plane. We find that the
longitudinal susceptibility diverges at the critical point, leading to the
behaviour qualitatively similar to the one which would result from non-zero
conductance of magnetic charges. We show that dynamics of critical fluctuations
belongs to the universality class of easy-axis ferroelectric and calculate
logarithmic corrections (within two-loop approximation) to the mean-field
critical behavior.Comment: 5 pages, 3 figures. Some misprints are corrected, among them are the
formula (20) and the estimation for $\Gamma_c
1/f Noise and Extreme Value Statistics
We study the finite-size scaling of the roughness of signals in systems
displaying Gaussian 1/f power spectra. It is found that one of the extreme
value distributions (Gumbel distribution) emerges as the scaling function when
the boundary conditions are periodic. We provide a realistic example of
periodic 1/f noise, and demonstrate by simulations that the Gumbel distribution
is a good approximation for the case of nonperiodic boundary conditions as
well. Experiments on voltage fluctuations in GaAs films are analyzed and
excellent agreement is found with the theory.Comment: 4 pages, 4 postscript figures, RevTe
Observable Signature of the Berezinskii-Kosterlitz-Thouless Transition in a Planar Lattice of Bose-Einstein Condensates
We investigate the possibility that Bose-Einstein condensates (BECs), loaded
on a 2D optical lattice, undergo - at finite temperature - a
Berezinskii-Kosterlitz-Thouless (BKT) transition. We show that - in an
experimentally attainable range of parameters - a planar lattice of BECs is
described by the XY model at finite temperature. We demonstrate that the
interference pattern of the expanding condensates provides the experimental
signature of the BKT transition by showing that, near the critical temperature,
the k=0 component of the momentum distribution and the central peak of the
atomic density profile sharply decrease. The finite-temperature transition for
a 3D optical lattice is also discussed, and the analogies with superconducting
Josephson junction networks are stressed through the text
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