Construction of bosonic symmetry-protected-trivial states and their topological invariants via G×SO(∞)G\times SO(\infty) non-linear σ\sigma-models

It has been shown that the L-type bosonic symmetry-protected-trivial (SPT) phases with pure gauge anomalous boundary can all be realized via non-linear $\sigma$-models (NL$\sigma$Ms) of the symmetry group $G$ with various topological terms. Those SPT phases (called the pure SPT phases) can be classified by group cohomology ${\cal H}^d(G,\mathbb{R}/\mathbb{Z})$. But there are also SPT phases with mixed gauge-gravity anomalous boundary (which will be called the mixed SPT phases). Some of the mixed SPT states were also referred as the beyond-group-cohomology SPT states. In this paper, we show that those beyond-group-cohomology SPT states are actually within another type of group cohomology classification. More precisely, we show that both the pure and the mixed SPT phases can be realized by $G\times SO(\infty)$ NL$\sigma$Ms with various topological terms. Through the group cohomology ${\cal H}^d[G\times SO(\infty),\mathbb{R}/\mathbb{Z}]$, we find that the set of our constructed L-type SPT phases in $d$-dimensional space-time are classified by $E^d(G)\rtimes \oplus_{k=1}^{d-1} {\cal H}^k(G,\text{iTO}_L^{d-k})\oplus {\cal H}^d(G,\mathbb{R}/\mathbb{Z})$ where $G$ may contain time-reversal. Here $\text{iTO}_L^d$ is the set of the L-type topologically-ordered phases in $d$-dimensional space-time that have no topological excitations, and one has $\text{iTO}_L^1=\text{iTO}_L^2=\text{iTO}_L^4=\text{iTO}_L^6=0$, $\text{iTO}_L^3=\mathbb{Z}$, $\text{iTO}_L^5=\mathbb{Z}_2$, $\text{iTO}_L^7=2\mathbb{Z}$. Our construction also gives us the topological invariants that fully characterize the corresponding SPT and iTO phases. Through several examples, we show how can the universal physical properties of SPT phases be obtained from those topological invariants.Comment: 39 pages, 10 figure. PRB versio

インドネシア産フトモモ科植物Baeckea frutescens由来の新規化合物の単離・構造決定と抗菌活性及び細胞毒性

富山大学・富医薬博甲216号・Khoirun Nisa・2016/9/7This doctoral thesis summarizes the full contents of the following publications.1) Nisa, K.; Ito, T.; Subehan.; Matsui, T.; Kodama, T.; Morita, H. New acylphloroglucinol derivatives from the leaves of Baeckea frutescens. Phytochemistry Letter 2016, 15, 42–45.2) Nisa, K.; Ito, T.; Kodama, T.; Tanaka, M.; Okamoto, Y.; Asakawa, Y.; Imagawa, H.; Morita, H. New cytotoxic phloroglucinols, baeckenones D–F, from the leaves of Indonesian Baeckea frutescens. Fitoterapia 2016, 109, 236–240.3) Ito, T.; Nisa, K.; Kodama, T.; Tanaka, M.; Okamoto, Y.; Ismail.; Morita, H. Two new cyclopentenones and a new furanone from Baeckea frutescens and their cytotoxicities. Fitoterapia 2016, 112, 132–135.富山大

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the classical Ito stochastic calculus. The existence result is based on the Yamada-Watanabe theorem.Comment: 21 page

Relativistic Langevin Dynamics in Expanding Media

We study the consequences of different realizations of diffusion processes in relativistic Langevin simulations. We elaborate on the Ito-Stratonovich dilemma by showing how microscopically calculated transport coefficients as obtained from a Boltzmann/Fokker-Planck equation can be implemented to lead to an unambiguous realization of the Langevin process. Pertinent examples within the pre-point (Ito) and post-point (H\"anggi-Klimontovich) Langevin prescriptions are worked out explicitly. Deviations from this implementation are shown to generate variants of the Boltzmann distribution as the stationary (equilibrium) solutions. Finally, we explicitly verify how the Lorentz invariance of the Langevin process is maintained in the presence of an expanding medium, including the case of an "elliptic flow" transmitted to a Brownian test particle. This is particularly relevant for using heavy-flavor diffusion as a quantitative tool to diagnose transport properties of QCD matter as created in ultrarelativistic heavy-ion collisions.Comment: 8 pages, 4 figures; v2: Reference adde

Synthesis of indium tin oxide nanoparticles by a nonhydrolytic sol-gel method

Indium tin oxide nanoparticles were synthesized in two different sizes by a nonhydrolytic sol-gel method. These powders were then transformed into ITO via an intermediate metastable state at between 300 and 600 ºC. The presence of characteristic O-In-O and O-Sn-O bands at 480 and 670 cm-1 confirmed the formation of ITO. The X-ray diffraction patterns indicated the preferential formation of metastable hexagonal phase ITO (corundum type) as opposed to cubic phase ITO when the reflux time was less than 3 h and the heat treatment temperature was below 600 ºC. Particle morphology and crystal size were examined by scanning electron microscopy

H ? filtering for stochastic singular fuzzy systems with time-varying delay

This paper considers the H? filtering problem for stochastic singular fuzzy systems with timevarying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is e?t - weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, e?t -weighted iISSiM and the H? attenuation level from disturbance to estimation error is belowa prescribed scalar.Aset of sufficient conditions for the solvability of the H? filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper