[en] We construct a family of quasi-solvable quantum many-body systems by an algebraic method. The models contain up to two-body interactions and have permutation symmetry. We classify these models under the consideration of invariance property. It turns out that this family includes the rational, hyperbolic (trigonometric) and elliptic Inozemtsev models as particular cases

[en] We construct a new family of N-fold supersymmetric systems which is referred to as 'type B'. A higher-derivative representation of the N-fold supercharge for this new family is given by a deformation of the type A N-fold supercharge. By utilizing the same method as in the sl(2) construction of type A N-fold supersymmetry, we show that this family includes two of the quasi-solvable models of Post-Turbiner type

[en] In a method of processing radioactive wastes by confining radioactive wastes by using solidified mortars, a resin incorporated mortar layer comprising fine aggregates (mountain sands or river sands having a grain size of less than 5mm), a synthetic resin (acryl resin) and a mixing material (calcium carbonate or silica sand powder) blended at a predetermined ratio is formed on the inner surface of a drum can. Then, after supplying the radioactive waste therein, a mortar filler having portland cement, a water reducer, aggregates and water blended at a predetermined ratio is in the drum can. This can certainly prevent intrusion of underground water and leakage of radioactivity, even if the drum can should suffer from corrosion when it is buried underground thereby enabling to confine them in the can stably for a long period of time. (T.M.)

[en] We propose a systematic method to construct quasi-solvable quantum many-body systems having permutation symmetry. By the introduction of elementary symmetric polynomials and suitable choice of a solvable sector, the algebraic structure of sl(M+1) naturally emerges. The procedure to solve the canonical-form condition for the two-body problem is presented in detail. It is shown that the resulting two-body quasi-solvable model can be uniquely generalized to the M-body system for arbitrary M under the consideration of the GL(2,K) symmetry. An intimate relation between quantum solvability and supersymmetry is found. With the aid of the GL(2,K) symmetry, we classify the obtained quasi-solvable quantum many-body systems. It turns out that there are essentially five inequivalent models of Inozemtsev type. Furthermore, we discuss the possibility of including M-body (M≥3) interaction terms without destroying the quasi-solvability

[en] We derive the necessary and sufficient condition for type A N-fold supersymmetry by direct calculation of the intertwining relation and show the complete equivalence between this analytic construction and the sl(2) construction based on quasi-solvability. An intimate relation between the pair of algebraic Hamiltonians is found. The classification problem on type A N-fold supersymmetric models is investigated by considering the invariance of both the Hamiltonians and N-fold supercharge under the GL(2,K) transformation. We generalize the Bender-Dunne polynomials to all the type A N-fold supersymmetric models without requiring the normalizability of the solvable sector. Although there is a case where weak orthogonality of them is not guaranteed, this fact does not cause any difficulty on the generalization. It is shown that the anti-commutator of the type A N-fold supercharges is expressed as the critical polynomial of them in the original Hamiltonian, from which we establish the complete type A N-fold superalgebra. A novel interpretation of the critical polynomials in view of polynomial invariants is given

[en] We provide a mathematical framework for PT-symmetric quantum theory, which is applicable irrespective of whether a system is defined on R or a complex contour, whether PT symmetry is unbroken, and so on. The linear space in which PT-symmetric quantum theory is naturally defined is a Krein space constructed by introducing an indefinite metric into a Hilbert space composed of square integrable complex functions in a complex contour. We show that in this Krein space every PT-symmetric operator is P-Hermitian if and only if it has transposition symmetry as well, from which the characteristic properties of the PT-symmetric Hamiltonians found in the literature follow. Some possible ways to construct physical theories are discussed within the restriction to the class K(H). (letter to the editor)

[en] In our previous work, we proposed a mathematical framework for PT-symmetric quantum theory, and in particular constructed a Krein space in which PT-symmetric operators would naturally act. In this work, we explore and discuss various general consequences and aspects of the theory defined in the Krein space, not only spectral properties and PT-symmetry breaking but also several issues, crucial for the theory to be physically acceptable, such as time evolution of state vectors, probability interpretation, uncertainty relation, classical-quantum correspondence, completeness, existence of a basis, and so on. In particular, we show that for a given real classical system we can always construct the corresponding PT-symmetric quantum system, which indicates that PT-symmetric theory in the Krein space is another quantization scheme rather than a generalization of the traditional Hermitian one in the Hilbert space. We propose a postulate for an operator to be a physical observable in this framework

[en] We formulate the framework of N-fold supersymmetry in one-body quantum mechanical systems with position-dependent mass (PDM). We show that some of the significant properties in the constant-mass case such as the equivalence to weak quasi-solvability also hold in the PDM case. We develop a systematic algorithm for constructing an N-fold supersymmetric PDM system. We apply it to obtain the type A N-fold supersymmetry in the case of PDM, which is characterized by the so-called type A monomial space. The complete classification and general form of effective potentials for the type A N-fold supersymmetry in the PDM case are given

[en] We present a set of necessary conditions for the existence of a biorthonormal basis composed of eigenvectors of non-Hermitian operators. As an illustration, we examine these conditions in the case of normal operators. We also provide a generalization of the conditions which is applicable to non-diagonalizable operators by considering not only eigenvectors but also all root vectors

[en] The authors analyzed dissolved constituents of 35 wells to investigate ground water movement in the Iwakura area, Kyoto city. The results were as follows: (1) The chemical composition of well waters was of SO₄^2-+Cl^--K⁺+Na⁺ and HCO₃^-- Ca²⁺-Mg²⁺ types. (2) The higher concentration of dissolved major inorganic constituents was detected in the area enclosed by contour lines between 110 and 130 meters, particularly an eastern part of the Nagatani stream. (3) The pattern of NH₄⁺-N and PO₄^3--P distributions was similar to that of major inorganic constituents, but the pattern of NO₃^--N distribution was completely similar to that of NH₄⁺-N and PO₄^3--P, and NO₂^--N was not present in almost all well waters. (4) The dissolved oxygen estimated on basis of dissolved argon was considerably unsaturated in well waters of eastern part of the Nagatani stream. (5) The dissolved nitrogen of a great number of wells was considerably unsaturated, and denitrification was found in a small number of wells. (6) By using simultaneous measurement of dissolved argon, the effective velosity of ground water ranged from 1.7 to 3.0 meters per day, corresponding to different hydraulic gradients. (author)