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Recently, hydrogen generation by water-splitting photocatalysts is attracting attention as a sustainable and clean energy resource. Photocatalytic hydrogen-generation systems are much simpler, cheaper, and easier to scale up than the coupled systems of electrolysis and solar cells, wind-power generation, etc. However, photocatalytic hydrogen generation is currently inefficient. This paper proposes the monolayer of boron phosphide as a stable highly-efficient water-splitting photocatalyst by high-precision density-functional theory calculations using a HSE06 functional with a solvent effect. The monolayer of boron phosphide has a direct allowed energy gap of about 1.4 eV, and functions as a one-step excitation photocatalyst. It absorbs sunlight with wavelengths below about 890 nm (ultraviolet, visible, and near-infrared light) and produces both hydrogen gas and oxygen gas from water at a suitable pH condition. By calculating the overpotentials of hydrogen and oxygen evolution reactions, its photocatalytic effectiveness was confirmed. The monolayers of boron phosphide will realize green hydrogen revolution.

We examine the Banados-Teitelboim-Zanelli (BTZ) black hole in terms of the information geometry and consider what kind of quantum information produces the black hole metric in close connection with the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. We find a Hessian potential that exactly produces both the BTZ metric and the entanglement entropy formula for CFT_{1+1} at a finite temperature. Taking a free-falling frame near the event horizon is a key procedure to derive these exact results. We also find an alternative Hessian potential that produces the same BTZ metric, which is found using the duality relation based on the Legendre transformation. We realize that the dual representation originates from the entanglement Hamiltonian on the CFT side. Our results suggest that the present information-geometrical approach is very powerful for understanding the mechanism of the holographic renormalization group such as the AdS/CFT correspondence., Comment: 13 pages

In this paper we treat the Law's effective Hamiltonian of the Dynamical Casimir Effect in a cavity and construct an analytic approximate solution of the time-dependent Schr{\"o}dinger equation under the general setting through a kind of rotating wave approximation (RWA). To the best of our knowledge this is the finest analytic approximate solution., Comment: Latex; 12 pages; no figure; minor changes (references updated). To appear in International Journal of Geometric Methods in Modern Physics

In this paper we treat the so-called dynamical Casimir effect in a cavity with a two--level atom and give an analytic approximate solution under the general setting. The aim of the paper is to show another approach based on Mathematical Physics to the paper [arXiv : 1112.0523 (quant-ph)] by A. V. Dodonov and V. V. Dodonov. We believe that our method is simple and beautiful., Comment: Latex ; 11 pages ; no figure ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics

In the preceding paper (arXiv:1103.0329 [math-ph]) we treated the Jaynes-Cummings model with dissipation and gave an approximate solution to the master equation for the density operator under the general setting by making use of the Zassenhaus expansion. However, to obtain a compact form of the approximate solution (which is in general complicated infinite series) is very hard when an initial condition is given. To overcome this difficulty we develop another approach and obtain a compact approximate solution when some initial condition is given., Comment: Latex ; 15 pages ; no figure

In this paper we treat the Jaynes-Cummings model with dissipation and give an approximate solution to the master equation for the density operator {\bf under the general setting} by making use of the Zassenhaus expansion., Comment: Latex ; 18 pages ; no figure. This is a paper based on hard calculation

The mobility of graphene is very high because the quantum Hall effects can be observed even at room temperature. Graphene has the potential of the material for novel devices because of this high mobility. But the energy gap of graphene is zero, so graphene can not be applied to semiconductor devices such as transistors, LEDs, etc. In order to control the energy gaps, we propose atomic monolayers which consist of various materials besides carbon atoms. To examine the energy dispersions of atomic monolayers of various materials, we calculated the electronic states of these atomic monolayers using density functional theory with structural optimizations. The quantum chemical calculation software "Gaussian 03" was used under periodic boundary conditions. The calculation method is LSDA/6-311G(d,p), B3LYP/6-31G(d), or B3LYP/6-311G(d,p). The calculated materials are C (graphene), Si (silicene), Ge, SiC, GeC, GeSi, BN, BP, BAs, AlP, AlAs, GaP, and GaAs. These atomic monolayers can exist in the flat honeycomb shapes. The energy gaps of these atomic monolayers take various values. Ge is a semimetal; AlP, AlAs, GaP, and GaAs are indirect semiconductors; and others are direct semiconductors. We also calculated the change of energy dispersions accompanied by the substitution of the atoms. Our results suggest that the substitution of impurity atoms for monolayer materials can control the energy gaps of the atomic monolayers. We conclude that atomic monolayers of various materials have the potential for novel devices., Comment: This paper was first presented at the 14th International Conference on Modulated Semiconductor Structures (MSS14) held in Kobe, Japan, on 23 July 2009

We describe calculations of Jarlskog's determinant in the case of n=3,4 in detail. Next, we investigate some formulas for invariant phases of unitary matrices and derive some explicit relations of them., Comment: 14pages, no figures

In the preceding paper (arXiv : 0710.2724 [quant-ph]) we have constructed the general solution for the master equation of quantum damped harmonic oscillator, which is given by the complicated infinite series in the operator algebra level. In this paper we give the explicit and compact forms to solutions (density operators) for some initial values. In particular, the compact one for the initial value based on a coherent state is given, which has not been given as far as we know. Moreover, some related problems are presented., Comment: Latex ; 8 pages ; no figure

In this note we give the most elementary method (as far as we know) to express $\zeta(2n+1)$ in terms of $\{\zeta(2k)|k\geq 1\}$. The method is based on only some elementary works by Leonhard Euler, so it is very instructive to non-experts or students., Comment: Latex ; 11 pages ; no figure ; typos corrected. This is our mathematical note

In this paper the general solution of the quantum damped harmonic oscillator is given., Comment: Latex ; 10 pages ; no figure ; typos corrected. The quantum damped harmonic oscillator is solved completely

In this paper the explicit flow representation to the Bose-Hubbard Hamiltonian is given in the general case. This representation may be useful in creating cat states for the system of atoms trapped in the optical ring., Comment: Latex ; 8 pages ; 1 figure ; minor changes

We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative Cayley-Hamilton's theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it has noncommutative entries. As examples, the noncommutative spectral decomposition and the exponential matrices of a quaternionic matrix and of a matrix with entries being harmonic oscillators are given., Comment: 18 pages, no figures

A closed expression to the Baker-Campbell-Hausdorff (B-C-H) formula in SO(4) is given by making use of the magic matrix by Makhlin. As far as we know this is the {\bf first nontrivial example} on (semi-) simple Lie groups summing up all terms in the B-C-H expansion., Comment: Latex ; 11 pages ; 1 figure ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.5 or 6), 2007

In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes entanglements in the case of $n=2$ is studied, and a clear-cut calculation of the universal Yang-Mills action in (hep-th/0602204) is given for the abelian case., Comment: Latex ; 19 pages ; 5 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.3)

The usual action of Yang-Mills theory is given by the quadratic form of curvatures of a principal G bundle defined on four dimensional manifolds. The non-linear generalization which is known as the Born-Infeld action has been given. In this paper we give another non-linear generalization on four dimensional manifolds and call it a universal Yang-Mills action. The advantage of our model is that the action splits {\bf automatically} into two parts consisting of self-dual and anti-self-dual directions. Namely, we have automatically the self-dual and anti-self-dual equations without solving the equations of motion as in a usual case. Our method may be applicable to recent non-commutative Yang-Mills theories studied widely., Comment: Latex file ; 14 pages ; 1 figure ; minor changes

To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\otimes a+S_{-}\otimes a^{\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\equiv S_{+}\otimes a+S_{-}\otimes a^{\dagger}$ diagonal to calculate ${e}^{-itgA}$ and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is first nontrivial examples as far as we know, and reproduce the calculations of ${e}^{-itgA}$ given in quant-ph/0404034. We also give a hint to an application to a noncommutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the noncommutativity of operators in quantum physics. Our method may open a new point of view in Mathematical Physics or Quantum Physics., Comment: Latex files, 21 pages; minor changes. To appear in International Journal of Geometric Methods in Modern Physics

In this letter the explicit form of evolution operator of the Tavis-Cummings model with three and four atoms is given. This is an important progress in quantum optics or mathematical physics., Comment: Latex file, 10 pages. We combined quant-ph/0404034(the three atoms case) and quant-ph/0406184(the four atoms case) into an article. to appear in International Journal of Geometric Methods in Modern Physics

In this letter the explicit form of evolution operator for the four atoms Tavis-Cummings model is given., Comment: Latex file, 6 pages

In this letter the explicit form of evolution operator of three atoms Tavis-Cummings model is given, which is a generalization of the paper quant-ph/0403008., Comment: Latex file, 9 pages. misprints corrected

For the creation operator $\adag $ and the annihilation operator $a$ of a harmonic oscillator, we consider Weyl ordering expression of $(\adag a)^n$ and obtain a new symmetric expression of Weyl ordering w.r.t. $\adag a \equiv N$ and $a\adag =N+1$ where $N$ is the number operator. Moreover, we interpret intertwining formulas of various orderings in view of the difference theory. Then we find that the noncommutative parameter corresponds to the increment of the difference operator w.r.t. variable $N$. Therefore, quantum (noncommutative) calculations of harmonic oscillators are done by classical (commutative) ones of the number operator by using the difference theory. As a by-product, nontrivial relations including the Stirling number of the first kind are also obtained., Comment: 15 pages, Latex2e, the title before replacement is "Orderings of Operators in Quantum Physics", new proofs by using a difference operator added, some references added, to appear in Modern Physics Letters A

In this thesis, we investigate various integral submodels and generalize them. In part I, we study the submodel of the nonlinear $\mathbf{C}P^1$-model and the related submodels in $(1+2)$ dimensions. In part II, we construct integrable submodels of the nonlinear Grassmann models in any dimension. We call them the Grassmann submodels. To show that our submodels are integrable, we construct an infinite number of conserved currents in two ways. One is that we make full use of the Noether currents of the nonlinear Grassmann models. The other is that we use a method of multiplier. Next we investigate symmetries of the Grassmann submodel. By using the symmetries, we can construct a wide class of exact solutions for our submodels. In part III, keeping some properties of our submodels, we generalize our submodels to higher-order equations. First we prepare the Bell polynomials and the generalized Bell polynomials which play the most important roles in our theory of generalized submodels. Next we generalize the $\mathbf{C}P^1$-submodel to higher-order equations. Lastly we generalize the Grassmann submodel to higher-order equations. By using the generalized Bell polynomials, we can show that the generalized Grassmann submodels are also integrable. As a result, we obtain a hierarchy of systems of integrable equations in any dimension which includes Grassmann submodels. These results lead to the conclusion that the integrable structures of our generalized submodels are closely related to some fundamental properties of the Bell polynomials., Comment: Ph.D. Dissertation at Waseda University, 81 pages, LaTeX2e

We generalize the submodel of nonlinear CP^1 models. The generalized models include higher order derivatives. For the systems of higher order equations, we construct a B\"acklund-like transformation of solutions and an infinite number of conserved currents by using the Bell polynomials., Comment: 11 pages

A universal disentangling formula (such as the Baker-Campbell-Hausdorff one) for coherent states of Perelomov's type ($ |z \ra = \exp (z\Adag -\bar{z}A) |0 \ra $) which are defined for generalized oscillator algebras is given., Comment: 11 pages, Latex2e

In the preceding paper(hep-th/9806084), we constructed submodels of nonlinear Grassmann sigma models in any dimension and, moreover, an infinite number of conserved currents and a wide class of exact solutions. In this paper, we first construct almost all conserved currents for the submodels and all ones for the one of ${\bf C}P^1$-model. We next review the Smirnov and Sobolev construction for the equations of ${\bf C}P^1$-submodel and extend the equations, the S-S construction and conserved currents to the higher order ones., Comment: 13 pages, AMSLaTex; an new section and an appendix added

We first consider nonlinear Grassmann sigma models in any dimension and next construct their submodels. For these models we construct an infinite number of nontrivial conserved currents. Our result is independent of time-space dimensions and, therfore, is a full generalization of that of authors (Alvarez, Ferreira and Guillen). Our result also suggests that our method may be applied to other nonlinear sigma models such as chiral models, $G/H$ sigma models in any dimension., Comment: 11 pages, AMSLaTex

We give in this paper some formulas which are useful in the construction of nontrivial conserved currents for submodels of CP^1-model or QP^1-model in (1+2) dimensions. These are full generalization of our results in the previous paper (hep-th/9802105)., Comment: 9 pages, AMSLaTex

We treat in this paper non-linear sigma models such as $CP^1$-model, $QP^1$-model and etc, in 1+2 dimensions. For submodels of such ones we definitely construct an infinite number of nontrivial conserved currents. Our result is a generalization of that of authors (Alvarez, Ferreira and Guillen)., Comment: 14 pages, AMSLaTex

In this paper we introduce the $(n+2)$-dimensional Born-Infeld action with a dual field strength $\tilde{H}$. We compute the field equation by using Schur polynomials and give a soliton solution., Comment: 14 pages, Latex; section 1 and section 5 corrected, an appendix added