30 research outputs found
The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
The 8-parameter elliptic Sakai difference Painlevé equation admits a Lax formulation. We show that a suitable specialization of the Lax equation gives rise to the time-independent Schrödinger equation for the BC1 8-parameter 'relativistic' Calogero-Moser Hamiltonian due to van Diejen. This amounts to a generalization of previous results concerning the Painlevé-Calogero correspondence to the highest level in the two hierarchies
The sixth Painleve equation arising from D_4^{(1)} hierarchy
The sixth Painleve equation arises from a Drinfel'd-Sokolov hierarchy
associated with the affine Lie algebra of type D_4 by similarity reduction.Comment: 14 page
Similarity reduction of the modified Yajima-Oikawa equation
We study a similarity reduction of the modified Yajima-Oikawa hierarchy. The
hierarchy is associated with a non-standard Heisenberg subalgebra in the affine
Lie algebra of type A_2^{(1)}. The system of equations for self-similar
solutions is presented as a Hamiltonian system of degree of freedom two, and
admits a group of B\"acklund transformations isomorphic to the affine Weyl
group of type A_2^{(1)}. We show that the system is equivalent to a
two-parameter family of the fifth Painlev\'e equation.Comment: latex2e file, 18 pages, no figures; (v2)Introduction is modified.
Some typos are correcte
On a q-difference Painlev\'e III equation: II. Rational solutions
Rational solutions for a -difference analogue of the Painlev\'e III
equation are considered. A Determinant formula of Jacobi-Trudi type for the
solutions is constructed.Comment: Archive version is already official. Published by JNMP at
http://www.sm.luth.se/math/JNMP
Multi-indexed Wilson and Askey-Wilson Polynomials
As the third stage of the project multi-indexed orthogonal polynomials, we
present, in the framework of 'discrete quantum mechanics' with pure imaginary
shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials.
They are obtained from the original Wilson and Askey-Wilson polynomials by
multiple application of the discrete analogue of the Darboux transformations or
the Crum-Krein-Adler deletion of 'virtual state solutions' of type I and II, in
a similar way to the multi-indexed Laguerre, Jacobi and (q-)Racah polynomials
reported earlier.Comment: 30 pages. Three references added. To appear in J.Phys.A. arXiv admin
note: text overlap with arXiv:1203.586
Study of the Sigma-nucleus potential by the (pi^-,K^+) reaction on medium-to-heavy nuclear targets
In order to study the Sigma-nucleus optical potential, we measured inclusive
(pi^-,K^+) spectra on medium-to-heavy nuclear targets: CH_2, Si, Ni, In and Bi.
The CH_2 target was used to calibrate the excitation energy scale by using the
elementary process p + pi^- -> K^+ + Sigma^-, where the C spectrum was also
extracted. The calibration was done with +-0.1 MeV precision. The angular
distribution of the elementary cross section was measured, and agreed well with
the previous bubble chamber data, but with better statistics, and the
magnitudes of the cross sections of the measured inclusive (pi^-,K^+) spectra
were also well calibrated. All of the inclusive spectra were found to be
similar in shape at a region near to the Sigma^- binding energy threshold,
showing a weak mass-number dependence on the magnitude of the cross section.
The measured spectra were compared with a theoretical calculation performed
within the framework of the Distorted Wave Impulse Approximation (DWIA). It has
been demonstrated that a strongly repulsive \sig-nucleus potential with a
non-zero size of the imaginary part is required to reproduce the shape of the
measured spectra.Comment: 21 pages, 24 figures, submitted to PR
Measurement of neutrino oscillation by the K2K experiment
We present measurements of nu(mu) disappearance in K2K, the KEK to Kamioka long-baseline neutrino oscillation experiment. One-hundred and twelve beam-originated neutrino events are observed in the fiducial volume of Super-Kamiokande with an expectation of 158.1(-8.6)(+9.2) events without oscillation. A distortion of the energy spectrum is also seen in 58 single-ring muonlike events with reconstructed energies. The probability that the observations are explained by the expectation for no neutrino oscillation is 0.0015% (4.3 sigma). In a two-flavor oscillation scenario, the allowed Delta m(2) region at sin(2)2 theta=1 is between 1.9 and 3.5x10(-3) eV(2) at the 90% C.L. with a best-fit value of 2.8x10(-3) eV(2)