Zero-dimensional analogue of the global gauge anomaly

A zero-dimensional analogue of Witten's global gauge anomaly is considered. For example, a zero-dimensional reduction of the two-dimensional \SO(2N) Yang-Mills theory with a single Majorana-Weyl fermion in the fundamental representation suffers from this anomaly. Another example is a zero-dimensional reduction of two- and three-dimensional \SU(2N_c) Yang-Mills theories which couple to a single Majorana fermion in the adjoint representation. In this case, any expectation value is either indeterminate or infinite.Comment: 6 pages, uses PTPTeX.cls, the final version to appear in Prog. Theor. Phy

Non-Adiabatic Transition in Spin-Boson Model and Generalization of the Landau-Zener Formula

Non-adiabatic transitions are studied in a spin-boson model with multiple scattering points. In order to generalize the Landau-Zener formula, which describes the case of a single scattering point, we define an ``effective gap'' for a set of scattering points. The generalized formula agrees very well with numerical results of the non-adiabatic dynamics, which we obtained by a direct numerical method. This will make the Landau-Zener formula yet more useful in analyzing experimental data of magnetic-moment inversion.Comment: 17 pages, 18 figure

Frequency Distribution of Intense Rainfall in the Wards of Tokyo and Its Relationship with the Spatial Structure of Building Heights

This study presents the minute spatial structure of both the frequency of intense rainfall (data from the 1991 to 2002, except 1993, were used) and recent trends (15-25 years until 2002) in the special wards of the Tokyo Metropolis in summer (June to September), on the basis of hourly rainfall data from a dense rain-gauge network. As this is the first step in elucidating the relationship between the distribution of the frequency of intense rainfall and that of surface roughness in metropolitan Tokyo, the averaged number of building stories within a certain area, which is referred to as the smoothed building height (SBH), was assumed to be an alternative parameter when deciding surface roughness. The distribution of the ascending rate of SBH (hereafter, the ascending rate of SBH is referred to as ARS) for wind direction was calculated by varying the averaging area for SBH, in order to compare it to the distribution of intense rainfall frequency. The results are summarized as follows. The high-frequency areas of intense rainfall appear in the western to northern parts of the area comprising the wards and along the boundary between the Tokyo Metropolis and SaitamaPrefecture. The frequency of intense rainfall in these areas is two to three times as high as that in the eastern part of the area comprising the wards. Moreover, the maximum areas of intense rainfall frequency are localized in the western, northern to northwestern, and southern part of the area comprising the wards, corresponding to wind direction. These areas are situated 3-5 km from the leeward side of the area, where the ARS derived from the SBH at a 1-2 km scale islarge, that is, the vicinities of Shinjuku (SNJ), Ikebukuro (1KB), and Shibuya (SBY). Accordingly, we suggest that the large surface roughness due to high-rise buildings in the western part of the area comprising the wards has the effect of increasing the frequency of intense rainfall. The increasing trend of intense rainfall is clear in the western part of the area comprising the wards, whereas a decreasing trend, although not statistically significant, is seen in the eastern part of the area comprising the wards. It is noted that observational stations with large increasing trends of intense rainfall, such as Nakano (NKN) and Shinagawa (SNG), are located 3-5 km from the leeward side of SNJ and on the shore of Tokyo Bay in the southern part of the area comprising the wards, respectively, where the ARS for easterly winds derived from the SBH at a 1-2 km scale is large

Discovery of antiferromagnetic chiral helical ordered state in trigonal GdNi3_3Ga9_9

We have performed magnetic susceptibility, magnetization, and specific heat measurements on a chiral magnet GdNi$_3$Ga$_9$, belonging to the trigonal space group $R32$ (\#155). A magnetic phase transition takes place at $T_{\rm N}$ = 19.5 K. By applying a magnetic field along the $a$ axis at 2 K, the magnetization curve exhibits two jumps at $\sim$ 3 kOe and = 45 kOe. To determine the magnetic structure, we performed a resonant X-ray diffraction experiment by utilizing a circularly polarized beam. It is shown that a long-period antiferromagnetic (AFM) helical order is realized at zero field. The Gd spins in the honeycomb layer are coupled in an antiferromagnetic manner in the $c$ plane and rotate with a propagation vector $q$ = (0, 0, 1.485). The period of the helix is 66.7 unit cells ($\sim 180$~nm). In magnetic fields above 3~kOe applied perpendicular to the helical $c$ axis, the AFM helical order changes to an AFM order with $q$ = (0, 0, 1.5).Comment: 7 pages, 12 figure

Overlap lattice fermion in a gravitational field

We construct a lattice Dirac operator of overlap type that describes the propagation of a Dirac fermion in an external gravitational field. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while it is believed that the general coordinate invariance is restored only in the continuum limit. Our doubler-free Dirac operator satisfies the conventional Ginsparg-Wilson relation and possesses gamma_5 hermiticity with respect to the inner product, which is suggested by the general coordinate invariance. The lattice index theorem in the presence of a gravitational field holds, and the classical continuum limit of the index density reproduces the Dirac genus. Reduction to a single Majorana fermion is possible for 8k+2 and 8k+4 dimensions, but not for 8k dimensions, which is consistent with the existence of the global gravitational/gauge anomalies in 8k dimensions. Other Lorentz representations, such as the spinor-vector and the bi-spinor representations, can also be treated. Matter fields with a definite chirality (with respect to the lattice-modified chiral matrix) are briefly considered.Comment: 22 pages, uses PTPTeX.cls, the final version to appear in Prog. Theor. Phy