Hard and Easy Instances of L-Tromino Tilings

We study tilings of regions in the square lattice with L-shaped trominoes. Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where it either remains NP-complete or has a polynomial time algorithm. First, we characterize the possibility of when an Aztec rectangle and an Aztec diamond has an L-tromino tiling. Then, we study tilings of arbitrary regions where only $180^\circ$ rotations of L-trominoes are available. For this particular case we show that deciding the existence of a tiling remains NP-complete; yet, if a region does not contains certain so-called "forbidden polyominoes" as sub-regions, then there exists a polynomial time algorithm for deciding a tiling.Comment: Full extended version of LNCS 11355:82-95 (WALCOM 2019

Noncoplanar spin canting in lightly-doped ferromagnetic Kondo lattice model on a triangular lattice

Effect of the coupling to mobile carriers on the 120$^\circ$ antiferromagnetic state is investigated in a ferromagnetic Kondo lattice model on a frustrated triangular lattice. Using a variational calculation for various spin orderings up to a four-site unit cell, we identify the ground-state phase diagram with focusing on the lightly-doped region. We find that an electron doping from the band bottom immediately destabilizes a 120$^\circ$ coplanar antiferromagnetic order and induces a noncoplanar three-sublattice ordering accompanied by an intervening phase separation. This noncoplanar phase has an umbrella-type spin configuration with a net magnetic moment and a finite spin scalar chirality. This spin-canting state emerges in competition between the antiferromagnetic superexchange interaction and the ferromagnetic double-exchange interaction under geometrical frustration. In contrast, a hole doping from the band top retains the 120$^\circ$-ordered state up to a finite doping concentration and does not lead to a noncolpanar ordering.Comment: 6 pages, 4 figures, accepted for publication in J. Phys.: Conf. Se

Photon generation by laser-Compton scattering at the KEK-ATF

We performed a photon generation experiment by laser-Compton scattering at the KEK-ATF, aiming to develop a Compton based polarized positron source for linear colliders. In the experiment, laser pulses with a 357 MHz repetition rate were accumulated and their power was enhanced by up to 250 times in the Fabry-Perot optical resonant cavity. We succeeded in synchronizing the laser pulses and colliding them with the 1.3 GeV electron beam in the ATF ring while maintaining the laser pulse accumulation in the cavity. As a result, we observed 26.0 +/- 0.1 photons per electron-laser pulse crossing, which corresponds to a yield of 10^8 photons in a second.Comment: 3 pages, 5 figures, Preprint submitted to TIPP09 Proceedings in NIM

Development of an intense positron source using a crystal--amorphous hybrid target for linear colliders

In a conventional positron source driven by a few GeV electron beam, a high amount of heat is loaded into a positron converter target to generate intense positrons required by linear colliders, and which would eventually damage the converter target. A hybrid target, composed of a single crystal target as a radiator of intense gamma--rays, and an amorphous converter target placed downstream of the crystal, was proposed as a scheme which could overcome the problem.This paper describes the development of an intense positron source with the hybrid target. A series of experiments on positron generation with the hybrid target has been carried out with a 8--GeV electron beam at the KEKB linac. We observed that positron yield from the hybrid target increased when the incident electron beam was aligned to the crystal axis and exceeded the one from the conventional target with the converter target of the same thickness, when its thickness is less than about 2 radiation length. The measurements in the temperature rise of the amorphous converter target was successfully carried out by use of thermocouples. These results lead to establishment to the evaluation of the hybrid target as an intense positron source.Comment: 17pages, 10figure

Radiative Corrections to Double Dalitz Decays: Effects on Invariant Mass Distributions and Angular Correlations

We review the theory of meson decays to two lepton pairs, including the cases of identical as well as non-identical leptons, as well as CP-conserving and CP-violating couplings. A complete lowest-order calculation of QED radiative corrections to these decays is discussed, and comparisons of predicted rates and kinematic distributions between tree-level and one-loop-corrected calculations are presented for both pi-zero and K-zero decays.Comment: 25 pages, 18 figures, added figures and commentar