arXiv subjects

Y. Kodama

Publications and source records attributed to Y. Kodama.

At least 19 recordsLinked to original sources

arXiv2021

Microscopic evidence for the intra-unit-cell electronic nematicity inside the pseudogap phase in YBa$_2$Cu$_4$O$_8$

Understanding the nature of the mysterious pseudogap phenomenon is one of the most important issues associated with cuprate high-$T_c$ superconductors. Here, we report $^{17}$O nuclear magnetic resonance (NMR) studies on two planar oxygen sites in stoichiometric cuprate YBa$_2$Cu$_4$O$_8$ to investigate the symmetry breaking inside the pseudogap phase. We observe that the Knight shifts of the two oxygen sites are identical at high temperatures but different below $T_{\rm nem} \sim$ 185 K, which is close to the pseudogap temperature $T^{\ast}$. Our result provides a microscopic evidence for intra-unit-cell electronic nematicity. The difference in quadrupole resonance frequency between the two oxygen sites is unchanged below $T_{\rm nem}$, which suggests that the observed nematicity does not directly stem from the local charge density modulation. Furthermore, a short-range charge density wave (CDW) order is observed below $T \simeq$ 150 K. The additional broadening in the $^{17}$O-NMR spectra because of this CDW order is determined to be inequivalent for the two oxygen sites, which is similar to that observed in case of nematicity. These results suggest a possible connection between nematicity, CDW order, and pseudogap.

cond-mat.str-el↗

arXiv2016

Optical Nonlinear Dark X-Waves

We introduce spatiotemporal optical dark X solitary waves of the (2+1)D {hyperbolic} nonlinear Schrödinger equation (NLSE), that rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between such NLSE and a well known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.

nlin.PS↗

arXiv2016

Optical Kerr Spatio-Temporal Dark-Lump Dynamics of Hydrodynamic Origin

There is considerable fundamental and applicative interest in obtaining non-diffractive and non-dispersive spatio-temporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatio-temporal dark lump solitary wave solutions of the (2+1)D nonlinear Schrödinger equation. Dark lumps represent multi-dimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2+1)D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical multidimensional extreme wave phenomena of hydrodynamic footprint.

nlin.PS↗

arXiv2016

Confluence of hypergeometric functions and integrable hydrodynamic type systems

It is known that a large class of integrable hydrodynamic type systems can be constructed through the Lauricella function, a generalization of the classical Gauss hypergeometric function. In this paper, we construct novel class of integrable hydrodynamic type systems which govern the dynamics of critical points of confluent Lauricella type functions defined on finite dimensional Grassmannian Gr(2,n), the set of 2xn matrices of rank two. Those confluent functions satisfy certain degenerate Euler-Poisson-Darboux equations. It is also shown that in general, hydrodynamic type system associated to the confluent Lauricella function is given by an integrable and non-diagonalizable quasi-linear system of a Jordan matrix form. The cases of Grassmannian Gr(2,5) for two component systems and Gr(2,6) for three component systems are considered in details.

nlin.SI↗

arXiv2015

Measurement and comparison of individual external doses of high-school students living in Japan, France, Poland and Belarus -- the "D-shuttle" project --

Twelve high schools in Japan (of which six are in Fukushima Prefecture), four in France, eight in Poland and two in Belarus cooperated in the measurement and comparison of individual external doses in 2014. In total 216 high-school students and teachers participated in the study. Each participant wore an electronic personal dosimeter "D-shuttle" for two weeks, and kept a journal of his/her whereabouts and activities. The distributions of annual external doses estimated for each region overlap with each other, demonstrating that the personal external individual doses in locations where residence is currently allowed in Fukushima Prefecture and in Belarus are well within the range of estimated annual doses due to the background radiation level of other regions/countries.

physics.med-ph↗

arXiv2014

Critical points, Lauricella functions and Whitham-type equations

A large class of semi-Hamiltonian systems of hydrodynamic type is interpreted as the equations governing families of critical points of functions obeying the classical linear Darboux equations for conjugate nets.The distinguished role of the Euler-Poisson-Darboux equations and associated Lauricella-type functions is emphasised. In particular, it is shown that the classical g-phase Whitham equations for the KdV and NLS equations are obtained via a g-fold iterated Darboux-type transformation generated by appropriate Lauricella functions.

nlin.SI↗

arXiv2010

Gamma-Ray Burst Polarimeter - GAP - aboard the Small Solar Power Sail Demonstrator IKAROS

The small solar power sail demonstrator "IKAROS" is a Japanese engineering verification spacecraft launched by H-IIA rocket on May 21, 2010 at JAXA Tanegashima Space Center. IKAROS has a huge sail with 20 m in diameter which is made of thin polyimide membrane. This sail converts the solar radiation-pressure into the propulsion force of IKAROS and accelerates the spacecraft. The Gamma-Ray Burst Polarimeter (GAP) aboard IKAROS is the first polarimeter to observe the gamma-ray polarization of Gamma-Ray Bursts (GRBs) during the IKAROS cruising phase. GAP is a tinny detector of 3.8 kg in weight and 17 cm in size with an energy range between 50-300 keV. The GAP detector also plays a role of the interplanetary network (IPN) to determine the GRB direction. The detection principle of gamma-ray polarization is the anisotropy of the Compton scattering. GAP works as the GRB polarimeter with the full coincidence mode between the central plastic and the surrounding CsI detectors. GAP is the first instrument, devoted for the observation of gamma-ray polarization in the astronomical history. In this paper, we present the GAP detector and its ground and onboard calibrations.

astro-ph.IM↗

arXiv2009

Uniform mixing of antiferromagnetism and high-T_c superconductivity in multilayered copper oxides Ba_2Ca_{n-1}Cu_nO_{2n}F_2 with apical fluorines (n=2,3,4): Cu-NMR/NQR and F-NMR

We report Cu-NMR/NQR and F-NMR studies on the multilayered high-T_c copper oxides Ba_2Ca_{n-1}Cu_nO_{2n}F_2 with n=2,3,4, where n is the number of CuO_2 planes. It is revealed that bi-layered Ba_2CaCu_2O_4F_2 is an underdoped superconductor with hole carriers, which are introduced into CuO_2 planes by an unexpected deviation from the nominal content of apical fluorines. In a previous paper, we proposed a self-doping mechanism as the origin of carrier doping in n=3 and n=4; in the mechanism, electrons are transferred from the inner CuO_2 plane (IP) to the outer one (OP). However, since it has been found that the bi-layered compound is hole doped, we have reexamined the superconducting and magnetic properties in n=3 and n=4 by Cu-NMR/NQR and F-NMR. The extensive NMR studies have confirmed that the apical-fluorine compounds are not self-doped but hole-doped, and that antiferromagnetism (AFM) and superconductivity (SC) coexist in a single CuO_2 plane. In n=4, the AFM ordering occurs at T_N = 80 K, well above T_c=55 K, where the respective AFM moments are M_AFM=0.11 mu_B and 0.18 mu_B at the OP and the IP. In n=3, on the other hand, the underdoped single IP exhibits a spontaneous moment M_AFM=0.12 mu_B at low temperatures and a peak in the nuclear-spin-lattice relaxation rate 1/T_1 of F at T_N=23 K, much lower than T_c = 76 K. We note that the increase in the number of IPs from one to two leads to an increase in T_N due to strengthening the interlayer coupling, although the doping levels for both compounds are almost comparable. The present results strongly suggest that the uniform mixing of AFM and SC is a general property inherent to a single CuO_2 plane in the underdoped regime for hole-doping.

cond-mat.supr-con↗

arXiv2009

Antiferromagnetic phase transition in four-layered high-T_c superconductors Ba_2Ca_3Cu_4O_8(F_yO_{1-y})_2 with T_c=55-102 K: Cu- and F-NMR studies

We report on magnetic characteristics in four-layered high-T_c superconductors Ba_2Ca_3Cu_4O_8(F_yO_{1-y})_2 with apical fluorine through Cu- and F-NMR measurements. The substitution of oxygen for fluorine at the apical site increases the carrier density (N_h) and T_c from 55 K up to 102 K. The NMR measurements reveal that antiferromagnetic order, which can uniformly coexist with superconductivity, exists up to N_h = 0.15, which is somewhat smaller than N_h = 0.17 being the quantum critical point (QCP) for five-layered compounds. The fact that the QCP for the four-layered compounds moves to a region of lower carrier density than for five-layered ones ensures that the decrease in the number of CuO_2 layers makes an interlayer magnetic coupling weaker.

cond-mat.supr-con↗

arXiv2007

Uniform Mixing of Antiferromagnetism and High-Tc Superconductivity in Electron-doped Layers in Four-layered Ba2Ca3Cu4O8F2 : A New Phenomenon in an Electron Underdoped RegimePhenomenon in an Electron Underdoped Regime

We report Cu- and F-NMR studies on a four-layered high-temperature superconductor Ba2Ca3Cu4O8F2(0234F(2.0)) with apical fluorine (F-1), an undoped 55 K-superconductor with a nominal Cu2+ valence on average. We reveal that this compound exhibits the antiferromagnetism (AFM) with a Neel temperature TN=100 K despite being a Tc= 55 K-superconductor. Through a comparison with a related tri-layered cuprate Ba2Ca2Cu3O6F2 (0223F(2.0)), it is demonstrated that electrons are transferred from the inner plane (IP) to the outer plane (OP) in 0234F(2.0) and 0223F(2.0), confirming the self-doped high-temperature superconductivity (HTSC) having electron and hole doping in a single compound. Remarlably, uniform mixing of AFM and HTSC takes place in both the electron-doped OPs and the hole-doped IPs in 0234F(2.0).

cond-mat.supr-con↗

arXiv2007

Geometry of the Pfaff lattices

Pfaff lattice was introduced by Adler and van Moerbeke to describe the partition functions for the random matrix models of GOE and GSE type. The partition functions of those matrix models are given by the Pfaffians of certain skew-symmetric matrices called the moment matrices, and they are the $τ$-functions of the Pfaff lattice. In this paper, we study a finite version of the Pfaff lattice equation as a Hamiltonian system. In particular, we prove the complete integrability in the sense of Arnold-Liouville, and using a moment map, we describe the real isospectral varieties of the Pfaff lattice. The image of the moment map is a convex polytope whose vertices are identified as the fixed points of the flow generated by the Pfaff lattice.

nlin.SI↗

arXiv2006

N-soliton solutions to the DKP equation and Weyl group actions

We study soliton solutions to the DKP equation which is defined by the Hirota bilinear form, \[ {\begin{array}{llll} (-4D_xD_t+D_x^4+3D_y^2) τ_n\cdotτ_n=24τ_{n-1}τ_{n+1}, (2D_t+D_x^3\mp 3D_xD_y) τ_{n\pm 1}\cdotτ_n=0 \end{array} \quad n=1,2,.... \] where $τ_0=1$. The $τ$-functions $τ_n$ are given by the pfaffians of certain skew-symmetric matrix. We identify one-soliton solution as an element of the Weyl group of D-type, and discuss a general structure of the interaction patterns among the solitons. Soliton solutions are characterized by $4N\times 4N$ skew-symmetric constant matrix which we call the $B$-matrices. We then find that one can have $M$-soliton solutions with $M$ being any number from $N$ to $2N-1$ for some of the $4N\times 4N$ $B$-matrices having only $2N$ nonzero entries in the upper triangular part (the number of solitons obtained from those $B$-matrices was previously expected to be just $N$).

nlin.SI↗

arXiv2006

Singular structure of Toda lattices and cohomology of certain compact Lie groups

We study the singularities (blow-ups) of the Toda lattice associated with a real split semisimple Lie algebra $\mathfrak g$. It turns out that the total number of blow-up points along trajectories of the Toda lattice is given by the number of points of a Chevalley group $K({\mathbb F}_q)$ related to the maximal compact subgroup $K$ of the group $\check G$ with $\check{\mathfrak g}={\rm Lie}(\check G)$ over the finite field ${\mathbb F}_q$. Here $\check{\mathfrak g}$ is the Langlands dual of ${\mathfrak g}$. The blow-ups of the Toda lattice are given by the zero set of the $τ$-functions. For example, the blow-ups of the Toda lattice of A-type are determined by the zeros of the Schur polynomials associated with rectangular Young diagrams. Those Schur polynomials are the $τ$-functions for the nilpotent Toda lattices. Then we conjecture that the number of blow-ups is also given by the number of real roots of those Schur polynomials for a specific variable. We also discuss the case of periodic Toda lattice in connection with the real cohomology of the flag manifold associated to an affine Kac-Moody algebra.

math.AG↗

arXiv2005

Integrable Quasiclassical Deformations of Cubic Curves

A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and characterize these deformations.

nlin.SI↗

arXiv2004

Integrable Deformations of Algebraic Curves

A general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations, is presented. We emphasize the use of several types of dynamical variables : branches, power sums and potentials.

nlin.SI↗

arXiv2002

Singular sector of the Burgers-Hopf hierarchy and deformations of hyperelliptic curves

We discuss the structure of shock singularities of the Burgers-Hopf hierarchy. It is shown that the set of singular solutions defines a stratification of the affine space of the flow parameters in the hierarchy. The stratification is associated with the Birkhoff decomposition of the Grassmannian given by the set of linear spaces spanned by the hierarchy. We then construct integrable hierarchy on each stratum and demonstrate that it describes a deformation of a hyperelliptic curve parametrizing the stratum. The hierarchy is called the hidden Burgers-Hopf hierarchy, and we found the Riemann invarint form and the hodograph solution.

nlin.SI↗

arXiv2002

Normal form and solitons

We present a review of the normal form theory for weakly dispersive nonlinear wave equations where the leading order phenomena can be described by the KdV equation. This is an infinite dimensional extension of the well-known Poincaré-Dulac normal form theory for ordinary differential equations. We also provide a detailed analysis of the interaction problem of solitary wavesas an important application of the normal form theory. Several explicit examples are discussed based on the normal form theory, and the results are compared with their numerical simulations. Those examples include the ion acoustic wave equation, the Boussinesq equation as a model of the shallow water waves, the regularized long wave equation and the Hirota bilinear equation having a 7th order linear dispersion.

nlin.SI↗

arXiv2002

Topology of the real part of hyperelliptic Jacobian associated with the periodic Toda lattice

This paper concerns the topology of the isospectral {\it real} manifold of the ${\mathfrak sl}(N)$ periodic Toda lattice consisting of $2^{N-1}$ different systems. The solutions of those systems contain blow-ups, and the set of those singular points defines a devisor of the manifold. Then adding the divisor, the manifold is compactified as the real part of the $(N-1)$-dimensional Jacobi variety associated with a hyperelliptic Riemann surface of genus $g=N-1$. We also study the real structure of the divisor, and then provide conjectures on the topology of the affine part of the real Jacobian and on the gluing rule over the divisor to compactify the manifold based upon the sign-representation of the Weyl group of ${\mathfrak sl}(N)$.

nlin.SI↗