994 research outputs found
On the boundary convergence of solutions to the Hermite-Schr\"odinger equation
In the half-space , we consider the
Hermite-Schr\"odinger equation ,
with given boundary values on .
We prove a formula that links the solution of this problem to that of the
classical Schr\"odinger equation. It shows that mixed norm estimates for the
Hermite-Schr\"odinger equation can be obtained immediately from those known in
the classical case. In one space dimension, we deduce sharp pointwise
convergence results at the boundary, by means of this link.Comment: 12 page
The Cole-Cole Law for Critical Dynamics in Glass-Forming Liquids
Within the mode-coupling theory (MCT) for glassy dynamics, the asymptotic
low-frequency expansions for the dynamical susceptibilities at critical points
are compared to the expansions for the dynamic moduli; this shows that the
convergence properties of the two expansions can be quite different. In some
parameter regions, the leading-order expansion formula for the modulus
describes the solutions of the MCT equations of motion outside the transient
regime successfully; at the same time, the leading- and next-to-leading order
expansion formulas for the susceptibility fail. In these cases, one can derive
a Cole-Cole law for the susceptibilities; and this law accounts for the
dynamics for frequencies below the band of microscopic excitations and above
the high-frequency part of the alpha-peak. It is shown that this scenario
explains the optical-Kerr-effect data measured for salol and benzophenone
(BZP). For BZP it is inferred that the depolarized light-scattering spectra
exhibit a wing for the alpha-peak within the Gigahertz band. This wing results
from the crossover of the von Schweidler-law part of the alpha-peak to the
high-frequency part of the Cole-Cole peak; and this crossover can be described
quantitatively by the leading-order formulas of MCT for the modulus.Comment: 15 pages, 9 figure
Pressure induced structural and dynamical changes in liquid Si. An ab-initio study
The static and dynamic properties of liquid Si at high-pressure have been
studied using the orbital free ab-initio molecular dynamics method. Four
thermodynamic states at pressures 4, 8, 14 and 23 GPa are considered. The
calculated static structure shows qualitative agreement with the available
experimental data. We analize the remarkable structural changes occurring
between 8 and 14 GPa along with its effect on several dynamic properties.Comment: 10 pages, 11 figures. Accepted for publication in Journal of Physics:
Condensed Matte
Density fluctuations and single-particle dynamics in liquid lithium
The single-particle and collective dynamical properties of liquid lithium
have been evaluated at several thermodynamic states near the triple point. This
is performed within the framework of mode-coupling theory, using a
self-consistent scheme which, starting from the known static structure of the
liquid, allows the theoretical calculation of several dynamical properties.
Special attention is devoted to several aspects of the single-particle
dynamics, which are discussed as a function of the thermodynamic state. The
results are compared with those of Molecular Dynamics simulations and other
theoretical approaches.Comment: 31 pages (in preprint format), 14 figures. Submitted to Phys. Rev.
Derivation of the nonlinear fluctuating hydrodynamic equation from underdamped Langevin equation
We derive the fluctuating hydrodynamic equation for the number and momentum
densities exactly from the underdamped Langevin equation. This derivation is an
extension of the Kawasaki-Dean formula in underdamped case. The steady state
probability distribution of the number and momentum densities field can be
expressed by the kinetic and potential energies. In the massless limit, the
obtained fluctuating hydrodynamic equation reduces to the Kawasaki-Dean
equation. Moreover, the derived equation corresponds to the field equation
derived from the canonical equation when the friction coefficient is zero.Comment: 16 page
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