11,830 research outputs found
Mode-Coupling Theory as a Mean-Field Description of the Glass Transition
Mode-coupling theory (MCT) is conjectured to be a mean-field description of
dynamics of the structural glass transition and the replica theory to be its
thermodynamic counterpart. However, the relationship between the two theories
remains controversial and quantitative comparison is lacking. In this Letter,
we investigate MCT for monatomic hard sphere fluids at arbitrary dimensions
above three and compare the results with replica theory. We find grave
discrepancies between the predictions of two theories. While MCT describes the
nonergodic parameter quantitatively better than the replica theory in three
dimension, it predicts a completely different dimension dependence of the
dynamical transition point. We find it to be due to the pathological behavior
of the nonergodic parameters derived from MCT, which exhibit negative tails in
real space at high dimensions.Comment: 5 pages, to appear in Phys. Rev. Lett.: Typos have been correcte
Thermodynamics and Structural Properties of the High Density Gaussian Core Model
We numerically study thermodynamic and structural properties of the
one-component Gaussian core model (GCM) at very high densities. The solid-fluid
phase boundary is carefully determined. We find that the density dependence of
both the freezing and melting temperatures obey the asymptotic relation, , , where is the number density, which
is consistent with Stillinger's conjecture. Thermodynamic quantities such as
the energy and pressure and the structural functions such as the static
structure factor are also investigated in the fluid phase for a wide range of
temperature above the phase boundary. We compare the numerical results with the
prediction of the liquid theory with the random phase approximation (RPA). At
high temperatures, the results are in almost perfect agreement with RPA for a
wide range of density, as it has been already shown in the previous studies. In
the low temperature regime close to the phase boundary line, although RPA fails
to describe the structure factors and the radial distribution functions at the
length scales of the interparticle distance, it successfully predicts their
behaviors at shorter length scales. RPA also predicts thermodynamic quantities
such as the energy, pressure, and the temperature at which the thermal
expansion coefficient becomes negative, almost perfectly. Striking ability of
RPA to predict thermodynamic quantities even at high densities and low
temperatures is understood in terms of the decoupling of the length scales
which dictate thermodynamic quantities from the interparticle distance which
dominates the peak structures of the static structure factor due to the
softness of the Gaussian core potential.Comment: 10 pages, 10 figure
Slow Dynamics of the High Density Gaussian Core Model
We numerically study crystal nucleation and glassy slow dynamics of the
one-component Gaussian core model (GCM) at high densities. The nucleation rate
at a fixed supersaturation is found to decrease as the density increases. At
very high densities, the nucleation is not observed at all in the time window
accessed by long molecular dynamics (MD) simulation. Concomitantly, the system
exhibits typical slow dynamics of the supercooled fluids near the glass
transition point. We compare the simulation results of the supercooled GCM with
the predictions of mode-coupling theory (MCT) and find that the agreement
between them is better than any other model glassformers studied numerically in
the past. Furthermore, we find that a violation of the Stokes-Einstein relation
is weaker and the non-Gaussian parameter is smaller than canonical
glassformers. Analysis of the probability distribution of the particle
displacement clearly reveals that the hopping effect is strongly suppressed in
the high density GCM. We conclude from these observations that the GCM is more
amenable to the mean-field picture of the glass transition than other models.
This is attributed to the long-ranged nature of the interaction potential of
the GCM in the high density regime. Finally, the intermediate scattering
function at small wavevectors is found to decay much faster than its self part,
indicating that dynamics of the large-scale density fluctuations decouples with
the shorter-ranged caging motion.Comment: 15 pages, 13 figure
A new effective Lagrangian for nuclear matter
The relativistic mean field model, the Zim\'anyi - Moszkowski (ZM) Lagrangian
describes nuclear matter and stable finite nuclei even in the non-relativistic
limit. It fails, however, to predict the correct non-relativistic spin-orbit
(SO) coupling. In this paper we improve on this matter by an additional tensor
coupling analogous to the anomalous gyromagnetic ratio. It can be adjusted to
describe the SO-term without changing the mean field solution of the
ZM-Lagrangian for nuclear matter.Comment: 8 pages LaTe
Halo-Galaxy Lensing: A Full Sky Approach
The halo-galaxy lensing correlation function or the average tangential shear
profile over sampled halos is a very powerful means of measuring the halo
masses, the mass profile, and the halo-mass correlation function of very large
separations in the linear regime. We reformulate the halo-galaxy lensing
correlation in harmonic space. We find that, counter-intuitively, errors in the
conventionally used flat-sky approximation remain at a % level even at very
small angles. The errors increase at larger angles and for lensing halos at
lower redshifts: the effect is at a few % level at the baryonic acoustic
oscillation scales for lensing halos of , and comparable with the
effect of primordial non-Gaussianity with at large
separations. Our results allow to readily estimate/correct for the full-sky
effect on a high-precision measurement of the average shear profile available
from upcoming wide-area lensing surveys.Comment: 12 pages, 4 figure
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