173 research outputs found
Dynamic Scaling of Width Distribution in Edwards--Wilkinson Type Models of Interface Dynamics
Edwards--Wilkinson type models are studied in 1+1 dimensions and the
time-dependent distribution, P_L(w^2,t), of the square of the width of an
interface, w^2, is calculated for systems of size L. We find that, using a flat
interface as an initial condition, P_L(w^2,t) can be calculated exactly and it
obeys scaling in the form _\infty P_L(w^2,t) = Phi(w^2 / _\infty,
t/L^2) where _\infty is the stationary value of w^2. For more complicated
initial states, scaling is observed only in the large- time limit and the
scaling function depends on the initial amplitude of the longest wavelength
mode. The short-time limit is also interesting since P_L(w^2,t) is found to
closely approximate the log-normal distribution. These results are confirmed by
Monte Carlo simulations on a `roof-top' model of surface evolution.Comment: 5 pages, latex, 3 ps figures in a separate files, submitted to
Phys.Rev.
Phase separation in fluids exposed to spatially periodic external fields
We consider the liquid-vapor type phase transition for fluids confined within
spatially periodic external fields. For a fluid in d=3 dimensions, the periodic
field induces an additional phase, characterized by large density modulations
along the field direction. At the triple point, all three phases (modulated,
vapor, and liquid) coexist. At temperatures slightly above the triple point and
for low (high) values of the chemical potential, two-phase coexistence between
the modulated phase and the vapor (liquid) is observed. We study this
phenomenon using computer simulations and mean-field theory for the Ising
model. The theory shows that, in order for the modulated phase to arise, the
field wavelength must exceed a threshold value. We also find an extremely low
tension of the interface between the modulated phase and the vapor/liquid
phases. The tension is of the order 10^{-4} kB T per squared lattice spacing,
where kB is the Boltzmann constant, and T the temperature. In order to detect
such low tensions, a new simulation method is proposed. We also consider the
case of d=2 dimensions. The modulated phase then does not survive, leading to a
radically different phase diagram.Comment: 11 pages, 14 figure
Viscoelasticity near the gel-point: a molecular dynamics study
We report on extensive molecular dynamics simulations on systems of soft
spheres of functionality f, i.e. particles that are capable of bonding
irreversibly with a maximum of f other particles. These bonds are randomly
distributed throughout the system and imposed with probability p. At a critical
concentration of bonds, p_c approximately equal to 0.2488 for f=6, a gel is
formed and the shear viscosity \eta diverges according to \eta ~ (p_c-p)^{-s}.
We find s is approximately 0.7 in agreement with some experiments and with a
recent theoretical prediction based on Rouse dynamics of phantom chains. The
diffusion constant decreases as the gel point is approached but does not
display a well-defined power law.Comment: 4 pages, 4 figure
Short-range correlations in quark matter
We investigate the role of short-range correlations in quark matter within
the framework of the SU(2) NJL model. Employing a next-to-leading order
expansion in 1/N_c for the quark self energy we construct a fully
self-consistent model that is based on the relations between spectral functions
and self energies. In contrast to the usual quasiparticle approximations we
take the collisional broadening of the quark spectral function consequently
into account. Mesons are dynamically generated in the fashion of a random phase
approximation, using full in-medium propagators in the quark loops. The results
are self-consistently fed back into the quark self energy. Calculations have
been performed for finite chemical potentials at zero temperature. The
short-range correlations do not only generate finite widths in the spectral
functions but also have influence on the chiral phase transition.Comment: 40 pages, 23 figures; revised and extended paper, accepted for
publication in Phys. Rev.
Optimal Vertex Cover for the Small-World Hanoi Networks
The vertex-cover problem on the Hanoi networks HN3 and HN5 is analyzed with
an exact renormalization group and parallel-tempering Monte Carlo simulations.
The grand canonical partition function of the equivalent hard-core repulsive
lattice-gas problem is recast first as an Ising-like canonical partition
function, which allows for a closed set of renormalization group equations. The
flow of these equations is analyzed for the limit of infinite chemical
potential, at which the vertex-cover problem is attained. The relevant fixed
point and its neighborhood are analyzed, and non-trivial results are obtained
both, for the coverage as well as for the ground state entropy density, which
indicates the complex structure of the solution space. Using special
hierarchy-dependent operators in the renormalization group and Monte-Carlo
simulations, structural details of optimal configurations are revealed. These
studies indicate that the optimal coverages (or packings) are not related by a
simple symmetry. Using a clustering analysis of the solutions obtained in the
Monte Carlo simulations, a complex solution space structure is revealed for
each system size. Nevertheless, in the thermodynamic limit, the solution
landscape is dominated by one huge set of very similar solutions.Comment: RevTex, 24 pages; many corrections in text and figures; final
version; for related information, see
http://www.physics.emory.edu/faculty/boettcher
Equivalence of the Falicov-Kimball and Brandt-Mielsch forms for the free energy of the infinite-dimensional Falicov-Kimball model
Falicov and Kimball proposed a real-axis form for the free energy of the
Falicov-Kimball model that was modified for the coherent potential
approximation by Plischke. Brandt and Mielsch proposed an imaginary-axis form
for the free energy of the dynamical mean field theory solution of the
Falicov-Kimball model. It has long been known that these two formulae are
numerically equal to each other; an explicit derivation showing this
equivalence is presented here.Comment: 4 pages, 1 figure, typeset with ReVTe
Super-roughening versus intrinsic anomalous scaling of surfaces
In this paper we study kinetically rough surfaces which display anomalous
scaling in their local properties such as roughness, or height-height
correlation function. By studying the power spectrum of the surface and its
relation to the height-height correlation, we distinguish two independent
causes for anomalous scaling. One is super-roughening (global roughness
exponent larger than or equal to one), even if the spectrum behaves non
anomalously. Another cause is what we term an intrinsically anomalous spectrum,
in whose scaling an independent exponent exists, which induces different
scaling properties for small and large length scales (that is, the surface is
not self-affine). In this case, the surface does not need to be super-rough in
order to display anomalous scaling. In both cases, we show how to extract the
independent exponents and scaling relations from the correlation functions, and
we illustrate our analysis with two exactly solvable examples. One is the
simplest linear equation for molecular beam epitaxy , well known to display
anomalous scaling due to super-roughening. The second example is a random
diffusion equation, which features anomalous scaling independent of the value
of the global roughness exponent below or above one.Comment: 9 pages, 6 figures, Revtex (uses epsfig), Phys. Rev. E, submitte
Spin-spin interaction and spin-squeezing in an optical lattice
We show that by displacing two optical lattices with respect to each other,
we may produce interactions similar to the ones describing ferro-magnetism in
condensed matter physics. We also show that particularly simple choices of the
interaction lead to spin-squeezing, which may be used to improve the
sensitivity of atomic clocks. Spin-squeezing is generated even with partially,
and randomly, filled lattices, and our proposal may be implemented with current
technology.Comment: 4 pages, including 4 figure
Improved limits on nuebar emission from mu+ decay
We investigated mu+ decays at rest produced at the ISIS beam stop target.
Lepton flavor (LF) conservation has been tested by searching for \nueb via the
detection reaction p(\nueb,e+)n. No \nueb signal from LF violating mu+ decays
was identified. We extract upper limits of the branching ratio for the LF
violating decay mu+ -> e+ \nueb \nu compared to the Standard Model (SM) mu+ ->
e+ nue numub decay: BR < 0.9(1.7)x10^{-3} (90%CL) depending on the spectral
distribution of \nueb characterized by the Michel parameter rho=0.75 (0.0).
These results improve earlier limits by one order of magnitude and restrict
extensions of the SM in which \nueb emission from mu+ decay is allowed with
considerable strength. The decay \mupdeb as source for the \nueb signal
observed in the LSND experiment can be excluded.Comment: 10 pages, including 1 figure, 1 tabl
Charge-transfer metal-insulator transitions in the spin-one-half Falicov-Kimball model
The spin-one-half Falicov-Kimball model is solved exactly on an
infinite-coordination-number Bethe lattice in the thermodynamic limit. This
model is a paradigm for a charge-transfer metal-insulator transition where the
occupancy of localized and delocalized electronic orbitals rapidly changes at
the metal-insulator transition (rather than the character of the electronic
states changing from insulating to metallic as in a Mott-Hubbard transition).
The exact solution displays both continuous and discontinuous (first-order)
transitions.Comment: 22 pages including 4 figures(eps), RevTe
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