2,816 research outputs found
Localizations at infinity and essential spectrum of quantum Hamiltonians: I. General theory
We isolate a large class of self-adjoint operators H whose essential spectrum
is determined by their behavior at large x and we give a canonical
representation of their essential spectrum in terms of spectra of limits at
infinity of translations of H. The configuration space is an arbitrary abelian
locally compact not compact group.Comment: 63 pages. This is the published version with several correction
Origin of coherent structures in a discrete chaotic medium
Using as an example a large lattice of locally interacting Hindmarsh-Rose chaotic neurons, we disclose the origin of ordered structures in a discrete nonequilibrium medium with fast and slow chaotic oscillations. The origin of the ordering mechanism is related to the appearance of a periodic average dynamics in the group of chaotic neurons whose individual slow activity is significantly synchronized by the group mean field. Introducing the concept of a "coarse grain" as a cluster of neuron elements with periodic averaged behavior allows consideration of the dynamics of a medium composed of these clusters. A study of this medium reveals spatially ordered patterns in the periodic and slow dynamics of the coarse grains that are controlled by the average intensity of the fast chaotic pulsation
Coarsening in potential and nonpotential models of oblique stripe patterns
We study the coarsening of two-dimensional oblique stripe patterns by
numerically solving potential and nonpotential anisotropic Swift-Hohenberg
equations. Close to onset, all models exhibit isotropic coarsening with a
single characteristic length scale growing in time as . Further from
onset, the characteristic lengths along the preferred directions and
grow with different exponents, close to 1/3 and 1/2, respectively. In
this regime, one-dimensional dynamical scaling relations hold. We draw an
analogy between this problem and Model A in a stationary, modulated external
field. For deep quenches, nonpotential effects produce a complicated
dislocation dynamics that can lead to either arrested or faster-than-power-law
growth, depending on the model considered. In the arrested case, small isolated
domains shrink down to a finite size and fail to disappear. A comparison with
available experimental results of electroconvection in nematics is presented.Comment: 13 pages, 13 figures. To appear in Phys. Rev.
W4 theory for computational thermochemistry: in pursuit of confident sub-kJ/mol predictions
In an attempt to improve on our earlier W3 theory [J. Chem. Phys. {\bf 120},
4129 (2004)] we consider such refinements as more accurate estimates for the
contribution of connected quadruple excitations (), inclusion of
connected quintuple excitations (), diagonal Born-Oppenheimer
corrections (DBOC), and improved basis set extrapolation procedures. Revised
experimental data for validation purposes were obtained from the latest version
of the ATcT (Active Thermochemical Tables) Thermochemical Network. We found
that the CCSDTQCCSDT(Q) difference converges quite rapidly with the basis
set, and that the formula
1.10[CCSDT(Q)/cc-pVTZ+CCSDTQ/cc-pVDZCCSDT(Q)/cc-pVDZ] offers a very reliable
as well as fairly cost-effective estimate of the basis set limit
contribution. The largest contribution found in the present work is
on the order of 0.5 kcal/mol (for ozone). DBOC corrections are significant at
the 0.1 kcal/mol level in hydride systems. . Based on the accumulated
experience, a new computational thermochemistry protocol for first-and
second-row main-group systems, to be known as W4 theory, is proposed. Our W4
atomization energies for a number of key species are in excellent agreement
(better than 0.1 kcal/mol on average, 95% confidence intervals narrower than 1
kJ/mol) with the latest experimental data obtained from Active Thermochemical
Tables. A simple {\em a priori} estimate for the importance of post-CCSD(T)
correlation contributions (and hence a pessimistic estimate for the error in a
W2-type calculation) is proposed.Comment: J. Chem. Phys., in press; electronic supporting information available
at http://theochem.weizmann.ac.il/web/papers/w4.htm
Cyclic Statistics In Three Dimensions
While 2-dimensional quantum systems are known to exhibit non-permutation,
braid group statistics, it is widely expected that quantum statistics in
3-dimensions is solely determined by representations of the permutation group.
This expectation is false for certain 3-dimensional systems, as was shown by
the authors of ref. [1,2,3]. In this work we demonstrate the existence of
``cyclic'', or , {\it non-permutation group} statistics for a system of n
> 2 identical, unknotted rings embedded in . We make crucial use of a
theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch
relations for the automorphisms of the free product group on n elements.Comment: 13 pages, 1 figure, LaTex, minor page reformattin
Pattern formation without heating in an evaporative convection experiment
We present an evaporation experiment in a single fluid layer. When latent
heat associated to the evaporation is large enough, the heat flow through the
free surface of the layer generates temperature gradients that can destabilize
the conductive motionless state giving rise to convective cellular structures
without any external heating. The sequence of convective patterns obtained here
without heating, is similar to that obtained in B\'enard-Marangoni convection.
This work present the sequence of spatial bifurcations as a function of the
layer depth. The transition between square to hexagonal pattern, known from
non-evaporative experiments, is obtained here with a similar change in
wavelength.Comment: Submitted to Europhysics Letter
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