Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region

We investigate a simple model using the numerical simulation in the complex Langevin equation (CLE) and the analytical approximation with the Gaussian Ansatz. We find that the Gaussian Ansatz captures the essential and even quantitative features of the CLE results quite well including unwanted behavior in the unstable region where the CLE converges to a wrong answer. The Gaussian Ansatz is therefore useful for looking into this convergence problem and we find that the exact answer in the unstable region is nicely reproduced by another solution that is naively excluded from the stability condition. We consider the Gaussian probability distributions corresponding to multiple solutions along the Lefschetz thimble to discuss the stability and the locality. Our results suggest a prescription to improve the convergence of the CLE simulation to the exact answer.Comment: 10 pages, 10 figure

Chiral phase transition of bulk Abelian gauge theories in the Randall-Sundrum brane world

The chiral phase transition of strong-coupling Abelian gauge theories is investigated in the brane world. It is assumed that gauge boson propagates in an extra dimension, i.e. bulk gauge theories. The phase structure is analytically evaluated by using the low-energy effective theories. We also numerically solve the ladder Schwinger-Dyson equation for the full fermion propagator including Kaluza-Klein (KK) excitation modes of the gauge field. It is found that the chiral phase transition is of the second order, and the critical value of the coupling constant is obtained. The extra dimension has a large influence on the chiral phase transition for the Randall-Sundrum (RS) brane world. It is studied how the number of KK modes affect the chiral phase transition.Comment: 18 pages, 7 figures, REVTe

Tide gauge response to tsunamis: Measurements at 40 tide gauge stations in Japan

The responses of tide gauges to tsunamis are examined by in situ measurements at 40 stations in northeastern Japan. Recovery of water level in the tide well is measured after the water is drained or added to create a water level difference between the inside and outside of the wells. The recovery times for a 1 m water level difference, estimated from the observations, vary from station to station and range from 65 to 1300 sec. Tsunami waveforms on tide gauge records from the 1983 Japan Sea earthquake are corrected for the observed response. For those stations with the observed recovery times longer than 300 sec, the corrected waveforms differ significantly from the originals and reproduce the inundation heights near the tide gauge stations, indicating that the tide gauge system significantly distorted the tsunami waveforms. At such stations, the correction for the response is necessary for quantification of tsunamis. The recovery time is also computed hydraulically on the basis of the structure of the tide gauge system. The ratio of the observed time to the computed one ranges between 1 and 10 which is attributed to environmentally-induced change of the tide gauge system

Operator analysis of physical states on magnetized T2/ZNT^{2}/Z_{N} orbifolds

We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$. We can obtain the exact and analytical results which can be applicable for any larger values of the quantized magnetic flux M, and show that the (non-diagonalized) kinetic terms are generated via our formalism and the number of the surviving physical states are calculable in a rigorous manner by simply following usual procedures in linear algebra in any case. Our approach is very powerful when we try to examine properties of the physical states on (complicated) magnetized orbifolds $T^{2}/Z_{3}$, $T^{2}/Z_{4}$, $T^{2}/Z_{6}$ (and would be in other cases on higher-dimensional torus) and could be an essential tool for actual realistic model construction based on these geometries.Comment: 41 pages, 1 figur

Impact of the passive component structure for high efficiency and fast response POL using Power Supply on Chip

Power-SoC, which integrates MCU, power device, control circuits and passive devices on the same chip has been attracted attention. In this paper, we discuss the impact of passive component structure for high efficiency and fast response POL using 3D Power-SoC (Supply on Chip). We propose the optimal structure according to the switching frequency based on simulations