50,374 research outputs found
Finding Exponential Product Formulas of Higher Orders
In the present article, we review a continual effort on generalization of the
Trotter formula to higher-order exponential product formulas. The exponential
product formula is a good and useful approximant, particularly because it
conserves important symmetries of the system dynamics. We focuse on two
algorithms of constructing higher-order exponential product formulas. The first
is the fractal decomposition, where we construct higher-order formulas
recursively. The second is to make use of the quantum analysis, where we
compute higher-order correction terms directly. As interludes, we also have
described the decomposition of symplectic integrators, the approximation of
time-ordered exponentials, and the perturbational composition.Comment: 22 pages, 9 figures. To be published in the conference proceedings
''Quantum Annealing and Other Optimization Methods," eds. B.K.Chakrabarti and
A.Das (Springer, Heidelberg
Transverse momentum distribution with radial flow in relativistic diffusion model
Large transverse momentum distributions of identified particles observed at
RHIC are analyzed by a relativistic stochastic model in the three dimensional
(non-Euclidean) rapidity space. A distribution function obtained from the model
is Gaussian-like in radial rapidity. It can well describe observed transverse
momentum distributions. Estimation of radial flow is made from the
analysis of distributions for in Au + Au Collisions.
Temperatures are estimated from observed large distributions under the
assumption that the distribution function approaches to the Maxwell-Boltzmann
distribution in the lower momentum limit. Power-law behavior of large
distribution is also derived from the model.Comment: 7 pages, 5 figures and 6 table
Analyses of multiplicity distributions by means of the Modified Negative Binomial Distribution and its KNO scaling function
We analyze various data of multiplicity distributions by means of the
Modified Negative Binomial Distribution (MNBD) and its KNO scaling function,
since this MNBD explains the oscillating behavior of the cumulant moment
observed in e^+e^- annihilations, h-h collisions and e-p collisions. In the
present analyses, we find that the MNBD(discrete distributions) describes the
data of charged particles in e^+e^- annihilations much better than the Negative
Binomial Distribution (NBD). To investigate stochastic property of the MNBD, we
derive the KNO scaling function from the discrete distribution by using a
straightforward method and the Poisson transform. It is a new KNO function
expressed by the Laguerre polynomials. In analyses of the data by using the KNO
scaling function, we find that the MNBD describes the data better than the
gamma function.Thus, it can be said that the MNBD is one of useful formulas as
well as NBD.Comment: 12 pages, latex, 3 figure
Silicon nitride sintered body
The sintering of silicon carbide and it production are described. The method of production is by calcination in which molding is followed by sintering without compression. The invention improves the composition of the silicon carbide ceramic. Six examples of the invention are illustrated and discussed
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