Exact soliton solutions of spinor Bose-Einstein condensates

We study matter-wave solitons in Bose-Einstein condensates of ultracold gaseous atoms with spin degrees of freedom and present a class of exact solutions based on the inverse scattering method. The one-soliton solutions are classified with respect to the spin states. We analyze collisional effects between solitons in the same or different spin state(s), which reveals a very interesting possibility: we can manipulate the spin dynamics by controlling the parameters of colliding solitons.     

Higher order solutions of Lieb-Liniger integral equation

We study higher order solutions of Lieb-Liniger integral equation for a one-dimensional δ-function Bose gas. By use of the power series expansion method, the integral equation is solved and the correction terms which improve the Bogoliubov theory are calculated analytically in the weak coupling regime. Physical quantities such as the ground state energy and the chemical potential are represented by a dimensionless parameter γ=c/ρ, where c is the interaction strength and ρ is the number density of particles while the quasi-momentum distribution function is expressed in terms of a dimensionless parameter λ=c/K, where K is the cut-off momentum.     

Symmetrization of Nonsymmetric Macdonald Polynomials and Macdonald's Inner Product Identities

We study the Macdonald polynomials that give eigenstates of some quantum many-body system with long-range interactions. Scalar products of the nonsymmetric Macdonald polynomials are algebraically evaluated through their Rodrigues-type formulas. We present a new proof of Macdonald's inner product identities without recourse to the shift operators; that is, we calculate square norms of the Macdonald polynomials through Weyl-symmetrization of those of the nonsymmetric Macdonald polynomials.     

Surface electromagnetic waves in superconductors

Varying electromagnetic fields at the surface of a superconductor are studied by means of the boson method. It is found that the frequency of the surface electromagnetic waves satisfies a dispersion relation which is entirely controlled by the system itself.     

Angle-resolved photoemission spectroscopy of perovskite-type transition-metal oxides and their analyses using tight-binding band structure

Nowadays it has become feasible to perform angle-resolved photoemission spectroscopy (ARPES) measurements of transition-metal oxides with three-dimensional perovskite structures owing to the availability of high-quality single crystals of bulk and epitaxial thin films. In this article, we review recent experimental results and interpretation of ARPES data using empirical tight-binding band-structure calculations. Results are presented for SrVO₃ (SVO) bulk single crystals and La_{1? x} Sr _x FeO₃ (LSFO) and La_{1? x} Sr _x MnO₃ (LSMO) thin films. In the case of SVO, from comparison of the experimental results with calculated surface electronic structure, we concluded that the obtained band dispersions reflect the bulk electronic structure. The experimental band structures of LSFO and LSMO were analyzed assuming the G-type antiferromagnetic state and the ferromagnetic state, respectively. We also demonstrated that the intrinsic uncertainty of the electron momentum perpendicular to the crystal surface is important for the interpretation of the APRES results of three-dimensional materials.     

The SU(v) Calogero spin system

A one-dimensional quantum particle system in which particles with su(v) spins interact through inverse square interactions is introduced. We refer to it as the SU(v) Calogero spin system. Using the quantum inverse scattering method, we reveal algebraic structures of the system: hidden symmetry is the U(v) − SU(v) U(1) current algebra. This is consistent with the fact that the ground-state wave function is a solution of the Knizhnik-Zamolodchikov equation. Furthermore we show that the system has a higher symmetry, known as the w_{1 + ∞}-algebra. With this W-algebra we have a unified viewpoint on the integrable quantum particle systems with long-range interactions such as the Calogero type (1/x²-interactions) and Sutherland type (1/sin²x-interactions). The Yangian symmetry is briefly discussed.     

Shallow water waves over an uneven bottom and an inhomogeneous KP equation

Three-dimensional shallow water waves over an uneven bottom are considered. The depth is assumed to be slow in variation. As a model, an inhomogeneous Kadomtsev-Petviashvili equation is presented. Some reductions of this equation are used to describe deformation of a line soliton due to the depth change. The model equation is valid for a wide class of two-dimensional nonlinear waves in inhomogeneous systems.     

General theory of grain boundaries in crystal

Presented is a microscopic derivation of the theory of grain boundaries in crystal. Fundamental properties of the grain boundaries are also discussed.