Pseudo entropy and pseudo-Hermiticity in quantum field theories

In this paper, we explore the concept of pseudo R\'enyi entropy within the context of quantum field theories (QFTs). The transition matrix is constructed by applying operators situated in different regions to the vacuum state. Specifically, when the operators are positioned in the left and right Rindler wedges respectively, we discover that the logarithmic term of the pseudo R\'enyi entropy is necessarily real. In other cases, the result might be complex. We provide direct evaluations of specific examples within 2-dimensional conformal field theories (CFTs). Furthermore, we establish a connection between these findings and the pseudo-Hermitian condition. Our analysis reveals that the reality or complexity of the logarithmic term of pseudo R\'enyi entropy can be explained through this pseudo-Hermitian framework. Additionally, we investigate the divergent term of the pseudo R\'enyi entropy. Interestingly, we observe a universal divergent term in the second pseudo R\'enyi entropy within 2-dimensional CFTs. This universal term is solely dependent on the conformal dimension of the operator under consideration. For $n$-th pseudo R\'enyi entropy ($n\ge 3$), the divergent term is intricately related to the specific details of the underlying theory.Comment: 26+12 pages, many figure

Symposium no. 06 Paper no. 77 Presentation: poster 77-1

On the basis of knowledge about P-adsorption by soils, we succeeded to synthesize very effective P adsorbent (high performance P adsorbent: HPA) which can effectively remove P from water for avoiding eutrification of water bodies such as ponds and rivers. The materials of the HPA were the soil, especially the volcanic ash soil with high P-adsorbing ability, and the various sludges. Generally, these materials were added with ferrous sulfate, pelletized and baked at 500 C for 15 min. The HPA had much higher abilities to adsorb P and to resist against mechanical disintegration in water than the volcanic ash soil. These abilities are prerequisite for cheap and simple removal of P from flowing water by percolation through the column of the P-adsorbent. The used and P-saturated HPA could be utilized as an amendment of P-deficient soils or could be regenerated with dilute sulfuric acid for further use as a P-adsorbent. Consequently, various users in Japan have welcomed the HPA. In addition, the HPA and its derivatives could strongly adsorb As (III), As (V), F and some toxic heavy metals as well and could be used for removing these pollutants from our environments

Supercritical Fluid Microcellular Foaming of High-Hardness TPU via a Pressure-Quenching Process: Restricted Foam Expansion Controlled by Matrix Modulus and Thermal Degradation

High-hardness thermoplastic polyurethane (HD-TPU) presents a high matrix modulus, low-temperature durability, and remarkable abrasion resistance, and has been used in many advanced applications. However, the fabrication of microcellular HD-TPU foam is rarely reported in the literature. In this study, the foaming behavior of HD-TPU with a hardness of 75D was investigated via a pressure-quenching foaming process using CO2 as a blowing agent. Microcellular HD-TPU foam with a maximum expansion ratio of 3.9-fold, a cell size of 25.9 μm, and cell density of 7.8 × 108 cells/cm3 was prepared, where a high optimum foaming temperature of about 170 °C had to be applied with the aim of softening the polymer’s matrix modulus. However, the foaming behavior of HD-TPU deteriorated when the foaming temperature further increased to 180 °C, characterized by the presence of coalesced cells, microcracks, and a high foam density of 1.0 g/cm3 even though the crystal domains still existed within the matrix. The cell morphology evolution of HD-TPU foam was investigated by adjusting the saturation time, and an obvious degradation occurred during the high-temperature saturation process. A cell growth mechanism of HD-TPU foams in degradation environments was proposed to explain this phenomenon based on the gas escape through the defective matrix