1,278 research outputs found
Triviality of the prolongation algebra of the Kuramoto-Sivashinsky equation
The authors apply the well known Wahlquist-Estabrook prolongation technique to the Kuramoto-Sivashinsky equation. The prolongation algebra turns out to be trivial in the sense that it is commutative. This supports nonintegrability of the equation
A Generalized Duality Transformation of the Anisotropic Xy Chain in a Magnetic Field
We consider the anisotropic chain in a magnetic field with special
boundary conditions described by a two-parameter Hamiltonian. It is shown that
the exchange of the parameters corresponds to a similarity transformation,
which reduces in a special limit to the Ising duality transformation.Comment: 6 pages, LaTeX, BONN-HE-93-4
Ramsey-type microwave spectroscopy on CO ()
Using a Ramsey-type setup, the lambda-doublet transition in the level of the state of CO was measured to be 394 064 870(10)
Hz. In our molecular beam apparatus, a beam of metastable CO is prepared in a
single quantum level by expanding CO into vacuum and exciting the molecules
using a narrow-band UV laser system. After passing two microwave zones that are
separated by 50 cm, the molecules are state-selectively deflected and detected
1 meter downstream on a position sensitive detector. In order to keep the
molecules in a single level, a magnetic bias field is applied. We find
the field-free transition frequency by taking the average of the and transitions,
which have an almost equal but opposite Zeeman shift. The accuracy of this
proof-of-principle experiment is a factor of 100 more accurate than the
previous best value obtained for this transition
Reconstructed Rough Growing Interfaces; Ridgeline Trapping of Domain Walls
We investigate whether surface reconstruction order exists in stationary
growing states, at all length scales or only below a crossover length, . The later would be similar to surface roughness in growing crystal
surfaces; below the equilibrium roughening temperature they evolve in a
layer-by-layer mode within a crossover length scale , but are always
rough at large length scales. We investigate this issue in the context of KPZ
type dynamics and a checker board type reconstruction, using the restricted
solid-on-solid model with negative mono-atomic step energies. This is a
topology where surface reconstruction order is compatible with surface
roughness and where a so-called reconstructed rough phase exists in
equilibrium. We find that during growth, reconstruction order is absent in the
thermodynamic limit, but exists below a crossover length , and that this local order fluctuates critically. Domain walls become
trapped at the ridge lines of the rough surface, and thus the reconstruction
order fluctuations are slaved to the KPZ dynamics
Roughening Induced Deconstruction in (100) Facets of CsCl Type Crystals
The staggered 6-vertex model describes the competition between surface
roughening and reconstruction in (100) facets of CsCl type crystals. Its phase
diagram does not have the expected generic structure, due to the presence of a
fully-packed loop-gas line. We prove that the reconstruction and roughening
transitions cannot cross nor merge with this loop-gas line if these degrees of
freedom interact weakly. However, our numerical finite size scaling analysis
shows that the two critical lines merge along the loop-gas line, with strong
coupling scaling properties. The central charge is much larger than 1.5 and
roughening takes place at a surface roughness much larger than the conventional
universal value. It seems that additional fluctuations become critical
simultaneously.Comment: 31 pages, 9 figure
Anomalous Roughness in Dimer-Type Surface Growth
We point out how geometric features affect the scaling properties of
non-equilibrium dynamic processes, by a model for surface growth where
particles can deposit and evaporate only in dimer form, but dissociate on the
surface. Pinning valleys (hill tops) develop spontaneously and the surface
facets for all growth (evaporation) biases. More intriguingly, the scaling
properties of the rough one dimensional equilibrium surface are anomalous. Its
width, , diverges with system size , as
instead of the conventional universal value . This originates
from a topological non-local evenness constraint on the surface configurations.Comment: Published version in PR
Crossover Scaling Functions in One Dimensional Dynamic Growth Models
The crossover from Edwards-Wilkinson () to KPZ () type growth is
studied for the BCSOS model. We calculate the exact numerical values for the
and massgap for using the master equation. We predict
the structure of the crossover scaling function and confirm numerically that
and , with . KPZ type growth is
equivalent to a phase transition in meso-scopic metallic rings where attractive
interactions destroy the persistent current; and to endpoints of facet-ridges
in equilibrium crystal shapes.Comment: 11 pages, TeX, figures upon reques
Crossover from Isotropic to Directed Percolation
Directed percolation is one of the generic universality classes for dynamic
processes. We study the crossover from isotropic to directed percolation by
representing the combined problem as a random cluster model, with a parameter
controlling the spontaneous birth of new forest fires. We obtain the exact
crossover exponent at using Coulomb gas methods in 2D.
Isotropic percolation is stable, as is confirmed by numerical finite-size
scaling results. For , the stability seems to change. An intuitive
argument, however, suggests that directed percolation at is unstable and
that the scaling properties of forest fires at intermediate values of are
in the same universality class as isotropic percolation, not only in 2D, but in
all dimensions.Comment: 4 pages, REVTeX, 4 epsf-emedded postscript figure
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