348 research outputs found
Cooperative Origin of Low-Density Domains in Liquid Water
We study the size of clusters formed by water molecules possessing large
enough tetrahedrality with respect to their nearest neighbors. Using Monte
Carlo simulation of the SPC/E model of water, together with a geometric
analysis based on Voronoi tessellation, we find that regions of lower density
than the bulk are formed by accretion of molecules into clusters exceeding a
minimum size. Clusters are predominantly linear objects and become less compact
as they grow until they reach a size beyond which further accretion is not
accompanied by a density decrease. The results suggest that the formation of
"ice-like" regions in liquid water is cooperative.Comment: 16 pages, 6 figure
Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization
The space subdivision in cells resulting from a process of random nucleation
and growth is a subject of interest in many scientific fields. In this paper,
we deduce the expected value and variance of these distributions while assuming
that the space subdivision process is in accordance with the premises of the
Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the
time dependency of nucleation and growth rates. We have also developed an
approximate analytical cell size probability density function. Finally, we have
applied our approach to the distributions resulting from solid phase
crystallization under isochronal heating conditions
Role of Collective Mode for Optical Conductivity and Reflectivity in Quarter-Filled Spin-Density-Wave State
Taking account of a collective mode relevant to charge fluctuation, the
optical conductivity of spin-density-wave state has been examined for an
extended Hubbard model with one-dimensional quarter-filled band. We find that,
within the random phase approximation, the conductivity exhibits several peaks
at the frequency corresponding to the excitation energy of the commensurate
collective mode. When charge ordering appears with increasing inter-site
repulsive interactions, the main peak with the lowest frequency is reduced and
the effective mass of the mode is enhanced indicating the suppression of the
effect of the collective mode by charge ordering. It is also shown that the
reflectivity becomes large in a wide range of frequency due to the huge
dielectric constant induced by the collective mode.Comment: 11 pages, 16 figure
Antiferromagnetic Phases of One-Dimensional Quarter-Filled Organic Conductors
The magnetic structure of antiferromagnetically ordered phases of
quasi-one-dimensional organic conductors is studied theoretically at absolute
zero based on the mean field approximation to the quarter-filled band with
on-site and nearest-neighbor Coulomb interaction. The differences in magnetic
properties between the antiferromagnetic phase of (TMTTF)X and the spin
density wave phase in (TMTSF)X are seen to be due to a varying degrees of
roles played by the on-site Coulomb interaction. The nearest-neighbor Coulomb
interaction introduces charge disproportionation, which has the same spatial
periodicity as the Wigner crystal, accompanied by a modified antiferromagnetic
phase. This is in accordance with the results of experiments on (TMTTF)Br
and (TMTTF)SCN. Moreover, the antiferromagnetic phase of (DI-DCNQI)Ag
is predicted to have a similar antiferromagnetic spin structure.Comment: 8 pages, LaTeX, 4 figures, uses jpsj.sty, to be published in J. Phys.
Soc. Jpn. 66 No. 5 (1997
Functional central limit theorems for vicious walkers
We consider the diffusion scaling limit of the vicious walker model that is a
system of nonintersecting random walks. We prove a functional central limit
theorem for the model and derive two types of nonintersecting Brownian motions,
in which the nonintersecting condition is imposed in a finite time interval
for the first type and in an infinite time interval for
the second type, respectively. The limit process of the first type is a
temporally inhomogeneous diffusion, and that of the second type is a temporally
homogeneous diffusion that is identified with a Dyson's model of Brownian
motions studied in the random matrix theory. We show that these two types of
processes are related to each other by a multi-dimensional generalization of
Imhof's relation, whose original form relates the Brownian meander and the
three-dimensional Bessel process. We also study the vicious walkers with wall
restriction and prove a functional central limit theorem in the diffusion
scaling limit.Comment: AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for
publicatio
Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices
Spatially and temporally inhomogeneous evolution of one-dimensional vicious
walkers with wall restriction is studied. We show that its continuum version is
equivalent with a noncolliding system of stochastic processes called Brownian
meanders. Here the Brownian meander is a temporally inhomogeneous process
introduced by Yor as a transform of the Bessel process that is a motion of
radial coordinate of the three-dimensional Brownian motion represented in the
spherical coordinates. It is proved that the spatial distribution of vicious
walkers with a wall at the origin can be described by the eigenvalue-statistics
of Gaussian ensembles of Bogoliubov-deGennes Hamiltonians of the mean-field
theory of superconductivity, which have the particle-hole symmetry. We report
that the time evolution of the present stochastic process is fully
characterized by the change of symmetry classes from the type to the type
I in the nonstandard classes of random matrix theory of Altland and
Zirnbauer. The relation between the non-colliding systems of the generalized
meanders of Yor, which are associated with the even-dimensional Bessel
processes, and the chiral random matrix theory is also clarified.Comment: REVTeX4, 16 pages, 4 figures. v2: some additions and correction
Effect of nearest- and next-nearest neighbor interactions on the spin-wave velocity of one-dimensional quarter-filled spin-density-wave conductors
We study spin fluctuations in quarter-filled one-dimensional
spin-density-wave systems in presence of short-range Coulomb interactions. By
applying a path integral method, the spin-wave velocity is calculated as a
function of on-site (U), nearest (V) and next-nearest (V_2) neighbor-site
interactions. With increasing V or V_2, the pure spin-density-wave state
evolves into a state with coexisting spin- and charge-density waves. The
spin-wave velocity is reduced when several density waves coexist in the ground
state, and may even vanish at large V. The effect of dimerization along the
chain is also considered.Comment: REVTeX, 11 pages, 9 figure
- …