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Takao Suzuki

Publications and source records attributed to Takao Suzuki.

At least 19 recordsLinked to original sources
arXiv2026

Degenerations of the fourth order $q$-Garnier system arising from confluences in quivers

The $q$-Garnier system was first proposed by Sakai, and alternative directions for its discrete time evolutions were provided by Nagao and Yamada. Recently, it was shown that all of those evolution directions are derived from a birational representation of an extended affine Weyl group which arises from the cluster algebraic construction established by Masuda, Okubo and Tsuda. In this article, we investigate a degeneration structure of the fourth order $q$-Garnier system by using confluences in quivers.

math.RT↗
arXiv2026

Poisson structures for a similarity reduction of the Drinfeld-Sokolov hierarchy of type $A$

In this article we consider the Drinfeld-Sokolov hierarchy of type $A$ and its similarity reduction. Then the similarity reduction is expressed as $2$ types of Hamiltonian systems, one is with a Poisson bracket and another a Poisson bracket of canonical coordinates. We also investigate a connection between the similarity reduction and the isomonodromy deformation system.

nlin.SI↗
arXiv2023

The Borel transform of the WKB solution to the Pearcey system

We study the system of partial differential equations which characterizes the Pearcey integral from the viewpoint of the exact WKB analysis. It is shown that the Borel transform of the WKB solutions to the system can be written as a linear combination of the branches of an algebraic function of degree $4$. Moreover, some connection formulas for the system are given.

math.CA↗
arXiv2022

An affine Weyl group action on the basic hypergeometric series arising from the $q$-Garnier system

Recently, we formulated the $q$-Garnier system and its variations as translations of an extended affine Weyl group of type $A^{(1)}_{2n+1}\times A^{(1)}_1\times A^{(1)}_1$. On the other hand, those systems admit particular solutions in terms of the basic hypergeometric series ${}_{n+1}ϕ_n$. In this article, we investigate an action of the extended affine Weyl group on ${}_{n+1}ϕ_n$.

math.CA↗
arXiv2021

A Lax formulation of a generalized $q$-Garnier system

Recently, a birational representation of an extended affine Weyl group of type $A_{mn-1}^{(1)}\times A_{m-1}^{(1)}\times A_{m-1}^{(1)}$ was proposed with the aid of a cluster mutation. In this article we formulate this representation in a framework of a system of $q$-difference equations with $mn\times mn$ matrices. This formulation is called a Lax form and is used to derive a generalization of the $q$-Garnier system.

nlin.SI↗
arXiv2020

Generalized $q$-Painlevé VI systems of type $(A_{2n+1}+A_1+A_1)^{(1)}$ arising from cluster algebra

In this article we formulate a group of birational transformations which is isomorphic to an extended affine Weyl group of type $(A_{2n+1}+A_1+A_1)^{(1)}$ with the aid of mutations and permutations of vertices to a mutation-periodic quiver on a torus. This group provides a class of higher order generalizations of Jimbo-Sakai's $q$-Painlevé VI equation as translations on a root lattice. Then the known three systems are obtained again; the $q$-Garnier system, a similarity reduction of the lattice $q$-UC hierarchy and a similarity reduction of the $q$-Drinfeld-Sokolov hierarchy.

math.QA↗
arXiv2016

A reformulation of the generalized $q$-Painlevé VI system with $W(A^{(1)}_{2n+1})$ symmetry

In the previous work we introduced the higher order $q$-Painlevé system $q$-$P_{(n+1,n+1)}$ as a generalization of the Jimbo-Sakai's $q$-Painlevé VI equation. It is derived from a $q$-analogue of the Drinfeld-Sokolov hierarchy of type $A^{(1)}_{2n+1}$ and admits a particular solution in terms of the Heine's $q$-hypergeometric function ${}_{n+1}ϕ_n$. However the obtained system is insufficient as a generalization of $q$-$P_{\rm{VI}}$ due to some reasons. In this article we rewrite the system $q$-$P_{(n+1,n+1)}$ to a more suitable one.

math-ph↗
arXiv2016

A higher order Painlevé system in two variables and extensions of the Appell hypergeometric functions $F_1$, $F_2$ and $F_3$

In this article we propose an extension of Appell hypergeometric function $F_2$ (or equivalently $F_3$). It is derived from a particular solution of a higher order Painlevé system in two variables. On the other hand, an extension of Appell's $F_1$ was introduced by Tsuda. We also show that those two extensions are equivalent at the level of systems of linear partial differential equations.

math.CA↗
arXiv2014

Development of spatial inhomogeneity of internal magnetic field above $T_{\rm c}$ in Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_{8+δ}$ observed by longitudinal-field muon-spin-relaxation

Longitudinal-field muon-spin-relaxation measurements have revealed inhomogeneous distribution of the internal magnetic field at temperatures above the bulk superconducting (SC) transition temperature, $T_{\rm c}$, in slightly overdoped Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_{8+δ}$. The distribution width of the internal magnetic field, $Δ$, evolves continuously with decreasing temperature toward $T_{\rm c}$. The origin of the increase in $Δ$ is discussed in terms of the creation of SC domains in a sample.

cond-mat.supr-con↗
arXiv2013

Ground state of bond-disordered quasi-one-dimensional spin system (CH3)2CHNH3Cu(ClxBr1-x)3 with x = 0, 0.25 and 0.3

The ground state of the quasi-one-dimensional system with bond-disorder (CH3)2CHNH3Cu(ClxBr1-x)3 with x = 0, 0.25 and 0.3 has been investigated by muSR. The Fourier spectrum of electron spin fluctuation in x =0.25 and 0.3 obtained by LF-muSR technique shows that there exists a soft-mode toward a possible phase transition to an exotic phase such as Bose-glass. In gapped system with x = 0, the Fourier spectrum is totally different from the other two, indicating the existence of the quantum critical point at a finite x between 0 and 0.25.

cond-mat.stat-mech↗
arXiv2012

A class of higher order Painleve systems arising from integrable hierarchies of type A

A relationship between Painleve systems and infinite-dimensional integrable hierarchies is studied. We derive a class of higher order Painleve systems from Drinfeld-Sokolov (DS) hierarchies of type A by similarity reductions. This result allows us to understand some properties of Painleve systems, Hamiltonian structures, Lax pairs and affine Weyl group symmetries.

math.QA↗
arXiv2012

Microscopic phase separation in triangular-lattice quantum spin magnet kappa-(BEDT-TTF)2Cu2(CN)3 probed by muon spin relaxation

The ground state of the quantum spin system kappa-(BEDT-TTF)2Cu2(CN)3 in which antiferromagnetically-interacting S=1/2 spins are located on a nearly equilateral triangular lattice attracts considerable interest both from experimental and theoretical aspects, because a simple antiferromagnetic order may be inhibited because of the geometrical frustration and hence an exotic ground state is expected. Furthermore, recent two reports on the ground state of this system have made it further intriguing by showing completely controversial results; one indicates the gapless state and the other gapped. By utilizing microscopic probe of muSR, we have investigated its spin dynamics below 0.1 K, unveiling its microscopically phase separated ground state at zero field.

cond-mat.str-el↗
arXiv2011

Possibility of Horizontal Line Node in KFe$_2$As$_2$ Probed by Muon Spin Rotation

The anisotropy and temperature dependence of the magnetic field penetration depth in the iron-based superconductor KFe$_2$As$_2$ have been measured down to 20 mK by means of muon spin rotation. We have observed that the flux-line lattice forms triangular symmetry when we applied the field parallel to c-axis, suggesting the interaction between vortices should be isotropic. The temperature dependence of the penetration depth observd with an applied field parallel and perpendicular to c-axis are different. These results can be accounted for by a superconducting gap function with a horizontal line node in the basal plane.

cond-mat.supr-con↗