12,749 research outputs found
Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths
The problem of counting plane trees with edges and an even or an odd
number of leaves was studied by Eu, Liu and Yeh, in connection with an identity
on coloring nets due to Stanley. This identity was also obtained by Bonin,
Shapiro and Simion in their study of Schr\"oder paths, and it was recently
derived by Coker using the Lagrange inversion formula. An equivalent problem
for partitions was independently studied by Klazar. We present three parity
reversing involutions, one for unlabelled plane trees, the other for labelled
plane trees and one for 2-Motzkin paths which are in one-to-one correspondence
with Dyck paths.Comment: 8 pages, 4 figure
Stochastic Cluster Series expansion for quantum spin systems
In this paper we develop a cluster-variant of the Stochastic Series expansion
method (SCSE). For certain systems with longer-range interactions the SCSE is
considerably more efficient than the standard implementation of the Stochastic
Series Expansion (SSE), at low temperatures. As an application of this method
we calculated the T=0-conductance for a linear chain with a (diagonal) next
nearest neighbor interaction.Comment: 5 pages, 7 figure
The infrared spectra of very large, compact, highly symmetric, polycyclic aromatic hydrocarbons (PAHs)
The mid-infrared spectra of large PAHs ranging from C54H18 to C130H28 are
determined computationally using Density Functional Theory. Trends in the band
positions and intensities as a function of PAH size, charge and geometry are
discussed. Regarding the 3.3, 6.3 and 11.2 micron bands similar conclusions
hold as with small PAHs.
This does not hold for the other features. The larger PAH cations and anions
produce bands at 7.8 micron and, as PAH sizes increases, a band near 8.5 micron
becomes prominent and shifts slightly to the red. In addition, the average
anion peak falls slightly to the red of the average cation peak. The similarity
in behavior of the 7.8 and 8.6 micron bands with the astronomical observations
suggests that they arise from large, cationic and anionic PAHs, with the
specific peak position and profile reflecting the PAH cation to anion
concentration ratio and relative intensities of PAH size. Hence, the broad
astronomical 7.7 micron band is produced by a mixture of small and large PAH
cations and anions, with small and large PAHs contributing more to the 7.6 and
7.8 micron component respectively.
For the CH out-of-plane vibrations, the duo hydrogens couple with the solo
vibrations and produce bands that fall at wavelengths slightly different than
their counterparts in smaller PAHs. As a consequence, previously deduced PAH
structures are altered in favor of more compact and symmetric forms. In
addition, the overlap between the duo and trio bands may reproduce the
blue-shaded 12.8 micron profile.Comment: ApJ, 36 pages, 9 fig
Weak non-linearities and cluster states
We propose a scalable approach to building cluster states of matter qubits
using coherent states of light. Recent work on the subject relies on the use of
single photonic qubits in the measurement process. These schemes have a low
initial success probability and low detector efficiencies cause a serious
blowup in resources. In contrast, our approach uses continuous variables and
highly efficient measurements. We present a two-qubit scheme, with a simple
homodyne measurement system yielding an entangling operation with success
probability 1/2. Then we extend this to a three-qubit interaction, increasing
this probability to 3/4. We discuss the important issues of the overhead cost
and the time scaling, showing how these can be vastly improved with access to
this new probability range.Comment: 5 pages, to appear in Phys. Rev.
A contiuum model for low temperature relaxation of crystal steps
High and low temperature relaxation of crystal steps are described in a
unified picture, using a continuum model based on a modified expression of the
step free energy. Results are in agreement with experiments and Monte Carlo
simulations of step fluctuations and monolayer cluster diffusion and
relaxation. In an extended model where mass exchange with neighboring terraces
is allowed, step transparency and a low temperature regime for unstable step
meandering are found.Comment: Submitted to Phys.Rev.Let
Monodisperse self-assembly in a model with protein-like interactions
We study the self-assembly behaviour of patchy particles with `protein-like'
interactions that can be considered as a minimal model for the assembly of
viral capsids and other shell-like protein complexes. We thoroughly explore the
thermodynamics and dynamics of self assembly as a function of the parameters of
the model and find robust assembly of all target structures considered. Optimal
assembly occurs in the region of parameter space where a free energy barrier
regulates the rate of nucleation, thus preventing the premature exhaustion of
the supply of monomers that can lead to the formation of incomplete shells. The
interactions also need to be specific enough to prevent the assembly of
malformed shells, but whilst maintaining kinetic accessibility. Free-energy
landscapes computed for our model have a funnel-like topography guiding the
system to form the target structure, and show that the torsional component of
the interparticle interactions prevents the formation of disordered aggregates
that would otherwise act as kinetic traps.Comment: 11 pages; 10 figure
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