arXiv subjects

K. Takemura

Publications and source records attributed to K. Takemura.

5 recordsLinked to original sources

arXiv2013

Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case

The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the Pöschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of the Pöschl-Teller potential, we obtain several families of explicit and global solutions of certain second order Fuchsian differential equations with an apparent singularity of characteristic exponent -2 and -1. They form orthogonal polynomials over $x\in(-1,1)$ with weight functions of the form $(1-x)^α(1+x)^β/\{(ax+b)^4q(x)^2\}$, in which $q(x)$ is a polynomial in $x$.

math.CA↗

arXiv2012

Longitudinal magnetic excitation in KCuCl3 studied by Raman scattering under hydrostatic pressures

We measure Raman scattering in an interacting spin-dimer system KCuCl3 under hydrostatic pressures up to 5 GPa mediated by He gas. In the pressure-induced quantum phase, we observe a one-magnon Raman peak, which originates from the longitudinal magnetic excitationand is observable through the second-order exchange interaction Raman process. We report the pressure dependence of the frequency, halfwidth and Raman intensity of this mode.

cond-mat.str-el↗

arXiv2011

Na-Au intermetallic compounds formed under high pressure at room temperature

High-pressure powder x-ray diffraction experiments have revealed that sodium and gold react at room temperature and form new Na-Au intermetallic compounds under high pressure. We have identified four intermetallic phases up to 60 GPa. The first phase (phase I) is the known Na2Au with the tetragonal CuAl2-type structure. It changed to the second phase (phase II) at about 0.8 GPa, which has the composition Na3Au with the trigonal Cu3As-type or hexagonal Cu3P-type structure. Phase II further transformed to phase III at 3.6 GPa. Phase III has the same composition Na3Au with the cubic BiF3-type structure. Finally, phase III changed to phase IV at around 54 GPa. Phase IV gives broad diffraction peaks, indicating large structural disorder.

cond-mat.mtrl-sci↗

arXiv1998

Representations of the Quantum Toroidal Algebra on highest weight modules of the Quantum Affine Algebra of type gl(N)

A representation of the Quantum Toroidal Algebra of type sl(N) is constructed on every irreducible integrable highest weight module of the Quantum Affine Algebra of type gl(N). As an intermediate step in the construction, we obtain a quantum analogue of the classical level-rank duality, describing the reciprocal decomposition of the q-Fock space with respect to mutually commutative actions of U_q(gl(N)^) of level L, and U_q(sl(L)^) of level N.

math.QA↗

arXiv1997

Toroidal actions on level 1 modules of U_q(\hat{sl_n})

Recently Varagnolo and Vasserot established that the q-deformed Fock spaces due to Hayashi, and Kashiwara, Miwa and Stern, admit actions of the quantum toroidal algebra $U_q(sl_n,tor)$ (n > 2) with the level (0,1). In the present article we propose a more detailed proof of this fact then the one given by Varagnolo and Vasserot. The proof is based on certain non-trivial properties of Cherednik's commuting difference operators. The quantum toroidal action on the Fock space depends on a certain parameter. We find that with a specific choice of this parameter the action on the Fock spaces gives rise to the toroidal action on irreducible level-1 highest weight modules of the affine quantum algebra $U_q(\hat{sl}_n)$. Similarly, by a specific choice of the parameter, the level (1,0) vertex representation of the quantum toroidal algebra gives rise to a $U_q(sl_n,tor)$-module structure on irreducible level-1 highest weight $U_q(\hat{sl}_n)$-modules.

q-alg↗