2,799 research outputs found
Comment on "Recurrences without closed orbits"
In a recent paper Robicheaux and Shaw [Phys. Rev. A 58, 1043 (1998)]
calculate the recurrence spectra of atoms in electric fields with non-vanishing
angular momentum not equal to 0. Features are observed at scaled actions
``an order of magnitude shorter than for any classical closed orbit of this
system.'' We investigate the transition from zero to nonzero angular momentum
and demonstrate the existence of short closed orbits with L_z not equal to 0.
The real and complex ``ghost'' orbits are created in bifurcations of the
``uphill'' and ``downhill'' orbit along the electric field axis, and can serve
to interpret the observed features in the quantum recurrence spectra.Comment: 2 pages, 1 figure, REVTE
Mode-coupling theory for structural and conformational dynamics of polymer melts
A mode-coupling theory for dense polymeric systems is developed which
unifyingly incorporates the segmental cage effect relevant for structural
slowing down and polymer chain conformational degrees of freedom. An ideal
glass transition of polymer melts is predicted which becomes molecular-weight
independent for large molecules. The theory provides a microscopic
justification for the use of the Rouse theory in polymer melts, and the results
for Rouse-mode correlators and mean-squared displacements are in good agreement
with computer simulation results.Comment: 4 pages, 3 figures, Phys. Rev. Lett. in pres
Theoretical Analysis of the "Double-q" Magnetic Structure of CeAl2
A model involving competing short-range isotropic Heisenberg interactions is
developed to explain the "double-q" magnetic structure of CeAl. For
suitably chosen interactions, terms in the Landau expansion quadratic in the
order parameters explain the condensation of incommensurate order at
wavevectors in the star of (1/2 , 1/2 , 1/2), where
is the cubic lattice constant. We show that the fourth order terms in the
Landau expansion lead to the formation of the so-called "double-q" magnetic
structure in which long-range order develops simultaneously at two
symmetry-related wavevectors, in striking agreement with the magnetic structure
determinations. Based on the value of the ordering temperature and of the
Curie-Weiss of the susceptibility, we estimate that the nearest
neighbor interaction is ferromagnetic, with K and the
next-nearest neighbor interaction is antiferromagnetic with K.
We also briefly comment on the analogous phenomenon seen in the similar system
TmS.Comment: 22 pages, 6 figure
Structure of Colloid-Polymer Suspensions
We discuss structural correlations in mixtures of free polymer and colloidal
particles based on a microscopic, 2-component liquid state integral equation
theory. Whereas in the case of polymers much smaller than the spherical
particles the relevant polymer degree of freedom is the center of mass, for
polymers larger than the (nano-) particles conformational rearrangements need
to be considered. They have the important consequence that the polymer
depletion layer exhibits two widely different length scales, one of the order
of the particle radius, the other of the order of the polymer radius or the
polymer density screening length in dilute or semidilute concentrations,
respectively. Their consequences on phase stability and structural correlations
are discussed extensively.Comment: 37 pages, 17 figures; topical feature articl
Distorted Copulas: Constructions and Tail Dependence
Given a copula C, we examine under which conditions on an order isomorphism Ï of [0, 1] the distortion C Ï: [0, 1]2 â [0, 1], C Ï(x, y) = Ï{C[Ïâ1(x), Ïâ1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on Ï that ensures that any distortion of C by means of Ï is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails
Finite size scaling for quantum criticality using the finite-element method
Finite size scaling for the Schr\"{o}dinger equation is a systematic approach
to calculate the quantum critical parameters for a given Hamiltonian. This
approach has been shown to give very accurate results for critical parameters
by using a systematic expansion with global basis-type functions. Recently, the
finite element method was shown to be a powerful numerical method for ab initio
electronic structure calculations with a variable real-space resolution. In
this work, we demonstrate how to obtain quantum critical parameters by
combining the finite element method (FEM) with finite size scaling (FSS) using
different ab initio approximations and exact formulations. The critical
parameters could be atomic nuclear charges, internuclear distances, electron
density, disorder, lattice structure, and external fields for stability of
atomic, molecular systems and quantum phase transitions of extended systems. To
illustrate the effectiveness of this approach we provide detailed calculations
of applying FEM to approximate solutions for the two-electron atom with varying
nuclear charge; these include Hartree-Fock, density functional theory under the
local density approximation, and an "exact"' formulation using FEM. We then use
the FSS approach to determine its critical nuclear charge for stability; here,
the size of the system is related to the number of elements used in the
calculations. Results prove to be in good agreement with previous Slater-basis
set calculations and demonstrate that it is possible to combine finite size
scaling with the finite-element method by using ab initio calculations to
obtain quantum critical parameters. The combined approach provides a promising
first-principles approach to describe quantum phase transitions for materials
and extended systems.Comment: 15 pages, 19 figures, revision based on suggestions by referee,
accepted in Phys. Rev.
Topological effects in ring polymers: A computer simulation study
Unconcatenated, unknotted polymer rings in the melt are subject to strong
interactions with neighboring chains due to the presence of topological
constraints. We study this by computer simulation using the bond-fluctuation
algorithm for chains with up to N=512 statistical segments at a volume fraction
\Phi=0.5 and show that rings in the melt are more compact than gaussian chains.
A careful finite size analysis of the average ring size R \propto N^{\nu}
yields an exponent \nu \approx 0.39 \pm 0.03 in agreement with a Flory-like
argument for the topologica interactions. We show (using the same algorithm)
that the dynamics of molten rings is similar to that of linear chains of the
same mass, confirming recent experimental findings. The diffusion constant
varies effectively as D_{N} \propto N^{-1.22(3) and is slightly higher than
that of corresponding linear chains. For the ring sizes considered (up to 256
statistical segments) we find only one characteristic time scale \tau_{ee}
\propto N^{2.0(2); this is shown by the collapse of several mean-square
displacements and correlation functions onto corresponding master curves.
Because of the shrunken state of the chain, this scaling is not compatible with
simple Rouse motion. It applies for all sizes of ring studied and no sign of a
crossover to any entangled regime is found.Comment: 20 Pages,11 eps figures, Late
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