1,635,587 research outputs found
A new type of solution of the Schr\"odinger equation on a self-similar fractal potential
Scattering a quantum particle by a self-similar fractal potential on a Cantor
set is investigated. We present a new type of solution of the functional
equation for the transfer matrix of this potential, which was derived earlier
from the Schr\"odinger equation.Comment: Latex, 4 pages, 7 eps-figures; the old figures are renewed and new
ones are adde
Spectral variability of planetary nebulae and related objects
The results of long-term spectral observations were used to search for
changes in planetary nebulae and emission-line stars. Significant increase of
excitation degree is found in two objects: M1-6 and M1-11
Entanglement Generation in the Scattering of One-Dimensional Particles
This article provides a convenient framework for quantitative evaluation of
the entanglement generated when two structureless, distinguishable particles
scatter non-relativistically in one dimension. It explores how three factors
determine the amount of entanglement generated: the momentum distributions of
the incoming particles, their masses, and the interaction potential. Two
important scales emerge, one set by the kinematics and one set by the dynamics.
This method also provides two approximate analytic formulas useful for
numerical evaluation of entanglement and reveals an interesting connection
between purity, linear coordinate transformations, and momentum uncertainties.Comment: 11 pages, submitted to PR
Magnetic Properties and Thermal Entanglement on a Triangulated Kagome Lattice
The magnetic and entanglement thermal (equilibrium) properties in spin-1/2
Ising-Heisenberg model on a triangulated Kagome lattice are analyzed by means
of variational mean-field like treatment based on Gibbs-Bogoliubov inequality.
Because of the separable character of Ising-type exchange interactions between
the Heisenberg trimers the calculation of quantum entanglement in a
self-consistent field can be performed for each of the trimers individually.
The concurrence in terms of three qubit isotropic Heisenberg model in effective
Ising field is non-zero even in the absence of a magnetic field. The magnetic
and entanglement properties exhibit common (plateau and peak) features
observable via (antferromagnetic) coupling constant and external magnetic
field. The critical temperature for the phase transition and threshold
temperature for concurrence coincide in the case of antiferromagnetic coupling
between qubits. The existence of entangled and disentangled phases in saturated
and frustrated phases is established.Comment: 21 pages, 13 figure
Production of scalar molecules in radiative decays
The potentialities of the production of the scalar molecules in the
radiative decays are considered beyond the narrow resonance width
approximation. It is shown that $BR(\phi\rightarrow\gamma
f_0(a_0)\rightarrow\gamma\pi\pi(\pi\eta))\approx (1\div 2)\times 10^{-5}\
,\BR(\phi\rightarrow\gamma (f_0+a_0)\rightarrow\gamma K^+K^-)\alt 10^{-6}BR(\phi\rightarrow\gamma (f_0+a_0) \to \gamma K^0\bar K^0)\alt 10^{-8}\pi\pi\ ,\ \pi\eta\ ,\ K^+K^-\ ,\ K^0\bar K^0\phi\rightarrow\gamma
f_0(a_0)e^+e^-\rightarrow\gamma \pi^+\pi^-\phi$ meson mass region.Comment: 19 pages, revtex, 4 eps files of figure
Arnold Tongues and Feigenbaum Exponents of the Rational Mapping for Q-state Potts Model on Recursive Lattice: Q<2
We considered Q-state Potts model on Bethe lattice in presence of external
magnetic field for Q<2 by means of recursion relation technique. This allows to
study the phase transition mechanism in terms of the obtained one dimensional
rational mapping. The convergence of Feigenabaum and
exponents for the aforementioned mapping is investigated for the period
doubling and three cyclic window. We regarded the Lyapunov exponent as an order
parameter for the characterization of the model and discussed its dependence on
temperature and magnetic field. Arnold tongues analogs with winding numbers
w=1/2, w=2/4 and w=1/3 (in the three cyclic window) are constructed for Q<2.
The critical temperatures of the model are discussed and their dependence on Q
is investigated. We also proposed an approximate method for constructing Arnold
tongues via Feigenbaum exponent.Comment: 15 pages, 12 figure
Improved bounds on the number of ternary square-free words
Improved upper and lower bounds on the number of square-free ternary words
are obtained. The upper bound is based on the enumeration of square-free
ternary words up to length 110. The lower bound is derived by constructing
generalised Brinkhuis triples. The problem of finding such triples can
essentially be reduced to a combinatorial problem, which can efficiently be
treated by computer. In particular, it is shown that the number of square-free
ternary words of length n grows at least as 65^(n/40), replacing the previous
best lower bound of 2^(n/17).Comment: 17 pages, AMS LaTeX. Paper has been completely rewritten and
comprises new results on both lower and upper bounds. The Mathematica program
mentioned in the article can be downloaded at
http://mcs.open.ac.uk/ugg2/wordcomb/brinkhuistriples.
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