87,082 research outputs found
Majority-vote model on hyperbolic lattices
We study the critical properties of a non-equilibrium statistical model, the
majority-vote model, on heptagonal and dual heptagonal lattices. Such lattices
have the special feature that they only can be embedded in negatively curved
surfaces. We find, by using Monte Carlo simulations and finite-size analysis,
that the critical exponents , and are different
from those of the majority-vote model on regular lattices with periodic
boundary condition, which belongs to the same universality class as the
equilibrium Ising model. The exponents are also from those of the Ising model
on a hyperbolic lattice. We argue that the disagreement is caused by the
effective dimensionality of the hyperbolic lattices. By comparative studies, we
find that the critical exponents of the majority-vote model on hyperbolic
lattices satisfy the hyperscaling relation
, where is an
effective dimension of the lattice. We also investigate the effect of boundary
nodes on the ordering process of the model.Comment: 8 pages, 9 figure
Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models
Exact analyses are given for two three-dimensional lattice systems: A system
of close-packed dimers placed in layers of honeycomb lattices and a layered
triangular-lattice interacting domain wall model, both with nontrivial
interlayer interactions. We show that both models are equivalent to a 5-vertex
model on the square lattice with interlayer vertex-vertex interactions. Using
the method of Bethe ansatz, a closed-form expression for the free energy is
obtained and analyzed. We deduce the exact phase diagram and determine the
nature of the phase transitions as a function of the strength of the interlayer
interaction.Comment: 22 pages in Revtex, 6 PS files, submitted to PR
Ultraviolet photonic crystal laser
We fabricated two dimensional photonic crystal structures in zinc oxide films
with focused ion beam etching. Lasing is realized in the near ultraviolet
frequency at room temperature under optical pumping. From the measurement of
lasing frequency and spatial profile of the lasing modes, as well as the
photonic band structure calculation, we conclude that lasing occurs in the
strongly localized defect modes near the edges of photonic band gap. These
defect modes originate from the structure disorder unintentionally introduced
during the fabrication process.Comment: 4 pages, 4 figure
Pattern formation of indirect excitons in coupled quantum wells
Using a nonlinear Schr\"odinger equation including short-range two-body
attraction and three-body repulsion, we investigate the spatial distribution of
indirect excitons in semiconductor coupled quantum wells. The results obtained
can interpret the experimental phenomenon that annular exciton cloud first
contracts then expands when the number of confined excitons is increased in
impurity potential well, as observed by Lai \emph{et al.} [Lai ,
Science \textbf{303}, 503 (2004)]. In particular, the model reconciles the
patterns of exciton rings reported by Butov \emph{et al.} [Butov ,
Nature \textbf{418}, 751 (2002)]. At higher densities, the model predicts much
richer patterns, which could be tested by future experiments.Comment: 5 Revtex4 pages, 3 figure
Self-gravitating astrophysical mass with singular central density vibrating in fundamental mode
The fluid-dynamical model of a self-gravitating mass of viscous liquid with
singular density at the center vibrating in fundamental mode is considered in
juxtaposition with that for Kelvin fundamental mode in a homogeneous heavy mass
of incompressible inviscid liquid. Particular attention is given to the
difference between spectral formulae for the frequency and lifetime of -mode
in the singular and homogeneous models. The newly obtained results are
discussed in the context of theoretical asteroseismology of pre-white dwarf
stage of red giants and stellar cocoons -- spherical gas-dust clouds with dense
star-forming core at the center.Comment: Mod. Phys. Lett. A, Vol. 24, No. 40 (2009) pp. 3257-327
The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
We consider the dimer-monomer problem for the rectangular lattice. By mapping
the problem into one of close-packed dimers on an extended lattice, we rederive
the Tzeng-Wu solution for a single monomer on the boundary by evaluating a
Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by
identifying it as the product of the nonzero eigenvalues of the Kasteleyn
matrix.Comment: 4 Pages to appear in the Physical Review E (2006
Rotating Black Holes in Metric-Affine Gravity
Within the framework of metric-affine gravity (MAG, metric and an independent
linear connection constitute spacetime), we find, for a specific gravitational
Lagrangian and by using {\it prolongation} techniques, a stationary axially
symmetric exact solution of the vacuum field equations. This black hole
solution embodies a Kerr-deSitter metric and the post-Riemannian structures of
torsion and nonmetricity. The solution is characterized by mass, angular
momentum, and shear charge, the latter of which is a measure for violating
Lorentz invariance.Comment: 32 pages latex, 3 table
Secure quantum channels with correlated twin laser beams
This work is the development and analysis of the recently proposed quantum
cryptographic protocol, based on the use of the two-mode coherently correlated
states. The protocol is supplied with the cryptographic control procedures. The
quantum noise influence on the channel error properties is examined. State
detection features are proposed
- …