Taro Nagao
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Taro Nagao has a total of 17 co-authors. Here are the top co-authors by number of shared publications:
- Gernot Akemann
Bielefeld University
5 shared publications - Graziano Vernizzi
Department of Physics and Astronomy, Siena College, Loudonville, New York 12211, USA
2 shared publications - Hans-Jürgen Stöckmann
Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany
2 shared publications - Heiner Kohler
Instituto de Ciencia de Materiales de Madrid CSIC Sor Juana de la Cruz 3 28049 Cantoblanco Madrid Spain
2 shared publications - Iván Parra
Faculty of Physics, Bielefeld University, Bielefeld, Germany
2 shared publications - Mario Kieburg
University of Melbourne
2 shared publications
Latest Publications
- 20 November 2024
- Published by IOP Publishing in Physica Scripta
- Vol. 99 (12) , 125261
Two-dimensional Coulomb gas on an elliptic annulus
It is well-known that two-dimensional Coulomb gases at a special inverse temperature β = 2 can be analyzed by using the orthogonal polynomial method borrowed from the theory of random matrices. In this paper, such Coulomb gas molecules are studied when they are distributed on an elliptic annulus, and the asymptotic forms of the molecule correlation functions in the thermodynamic limit are evaluated. For that purpose, two-dimensional orthogonality relations of the Chebyshev polynomials on an elliptic annulus are utilized.
- 20 November 2024
- Published by IOP Publishing in Physica Scripta
- Vol. 99 (12) , 125261
Two-dimensional Coulomb gas on an elliptic annulus
It is well-known that two-dimensional Coulomb gases at a special inverse temperature β = 2 can be analyzed by using the orthogonal polynomial method borrowed from the theory of random matrices. In this paper, such Coulomb gas molecules are studied when they are distributed on an elliptic annulus, and the asymptotic forms of the molecule correlation functions in the thermodynamic limit are evaluated. For that purpose, two-dimensional orthogonality relations of the Chebyshev polynomials on an elliptic annulus are utilized.
- Open Access
- 18 September 2020
- Published by Springer Nature in Constructive Approximation
- Vol. 53 (3) , 441-478
Gegenbauer and Other Planar Orthogonal Polynomials on an Ellipse in the Complex Plane
We show that several families of classical orthogonal polynomials on the real line are also orthogonal on the interior of an ellipse in the complex plane, subject to a weighted planar Lebesgue measure. In particular these include Gegenbauer polynomials $$C_n^{(1+\alpha )}(z)$$ for $$\alpha >-1$$ containing the Legendre polynomials $$P_n(z)$$ and the subset $$P_n^{(\alpha +\frac{1}{2},\pm \frac{1}{2})}(z)$$ of the Jacobi polynomials. These polynomials provide an orthonormal basis and the corresponding weighted Bergman space forms a complete metric space. This leads to a certain family of Selberg integrals in the complex plane. We recover the known orthogonality of Chebyshev polynomials of the first up to fourth kind. The limit $$\alpha \rightarrow \infty $$ leads back to the known Hermite polynomials orthogonal in the entire complex plane. When the ellipse degenerates to a circle we obtain the weight function and monomials known from the determinantal point process of the ensemble of truncated unitary random matrices.- 18 September 2020
- Published by Springer Nature in Constructive Approximation
- Vol. 53 (3) , 441-478
Open AccessGegenbauer and Other Planar Orthogonal Polynomials on an Ellipse in the Complex Plane
We show that several families of classical orthogonal polynomials on the real line are also orthogonal on the interior of an ellipse in the complex plane, subject to a weighted planar Lebesgue measure. In particular these include Gegenbauer polynomials $$C_n^{(1+\alpha )}(z)$$ for $$\alpha >-1$$ containing the Legendre polynomials $$P_n(z)$$ and the subset $$P_n^{(\alpha +\frac{1}{2},\pm \frac{1}{2})}(z)$$ of the Jacobi polynomials. These polynomials provide an orthonormal basis and the corresponding weighted Bergman space forms a complete metric space. This leads to a certain family of Selberg integrals in the complex plane. We recover the known orthogonality of Chebyshev polynomials of the first up to fourth kind. The limit $$\alpha \rightarrow \infty $$ leads back to the known Hermite polynomials orthogonal in the entire complex plane. When the ellipse degenerates to a circle we obtain the weight function and monomials known from the determinantal point process of the ensemble of truncated unitary random matrices. - 22 January 2020
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 53 (7) , 075201
Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality
We investigate a one-parameter family of Coulomb gases in two dimensions, which are confined to an ellipse due to a hard wall constraint, and are subject to an additional external potential. At inverse temperature we can use the technique of planar orthogonal polynomials, borrowed from random matrix theory, to explicitly determine all k -point correlation functions for a fixed number of particles N . These are given by the determinant of the kernel of the corresponding orthogonal polynomials, which in our case are the Gegenbauer polynomials, or a subset of the asymmetric Jacobi polynomials, depending on the choice of external potential, as shown in a companion paper recently published by three of the authors. In the rotationally invariant case, when the ellipse becomes the unit disc, our findings agree with that of the ensemble of truncated unitary random matrices. The thermodynamical large- N limit is investigated in the local scaling regime in the bulk and at the edge of the spectrum at weak and strong non-Hermiticity. We find new universality classes in these limits and recover the sine- and Bessel-kernel in the Hermitian limit. The limiting global correlation functions of particles in the interior of the ellipse are more difficult to obtain but found in the special cases corresponding to the Chebyshev polynomials.
- 22 January 2020
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 53 (7) , 075201
Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality
We investigate a one-parameter family of Coulomb gases in two dimensions, which are confined to an ellipse due to a hard wall constraint, and are subject to an additional external potential. At inverse temperature we can use the technique of planar orthogonal polynomials, borrowed from random matrix theory, to explicitly determine all k -point correlation functions for a fixed number of particles N . These are given by the determinant of the kernel of the corresponding orthogonal polynomials, which in our case are the Gegenbauer polynomials, or a subset of the asymmetric Jacobi polynomials, depending on the choice of external potential, as shown in a companion paper recently published by three of the authors. In the rotationally invariant case, when the ellipse becomes the unit disc, our findings agree with that of the ensemble of truncated unitary random matrices. The thermodynamical large- N limit is investigated in the local scaling regime in the bulk and at the edge of the spectrum at weak and strong non-Hermiticity. We find new universality classes in these limits and recover the sine- and Bessel-kernel in the Hermitian limit. The limiting global correlation functions of particles in the interior of the ellipse are more difficult to obtain but found in the special cases corresponding to the Chebyshev polynomials.
- Open Access
Gegenbauer and other planar orthogonal polynomials on an ellipse in the complex plane
We show that several families of classical orthogonal polynomials on the real line are also orthogonal on the interior of an ellipse in the complex plane, subject to a weighted planar Lebesgue measure. In particular these include Gegenbauer polynomials $C_n^{(1+\alpha)}(z)$ for $\alpha>-1$ containing the Legendre polynomials $P_n(z)$, and the subset $P_n^{(\alpha+\frac12,\pm\frac12)}(z)$ of the Jacobi polynomials. These polynomials provide an orthonormal basis and the corresponding weighted Bergman space forms a complete metric space. This leads to a certain family of Selberg integrals in the complex plane. We recover the known orthogonality of Chebyshev polynomials of first up to fourth kind. The limit $\alpha\to\infty$ leads back to the known Hermite polynomials orthogonal in the entire complex plane. When the ellipse degenerates to a circle we obtain the weight function and monomials known from the determinantal point process of the ensemble of truncated unitary random matrices.Open AccessGegenbauer and other planar orthogonal polynomials on an ellipse in the complex plane
We show that several families of classical orthogonal polynomials on the real line are also orthogonal on the interior of an ellipse in the complex plane, subject to a weighted planar Lebesgue measure. In particular these include Gegenbauer polynomials $C_n^{(1+\alpha)}(z)$ for $\alpha>-1$ containing the Legendre polynomials $P_n(z)$, and the subset $P_n^{(\alpha+\frac12,\pm\frac12)}(z)$ of the Jacobi polynomials. These polynomials provide an orthonormal basis and the corresponding weighted Bergman space forms a complete metric space. This leads to a certain family of Selberg integrals in the complex plane. We recover the known orthogonality of Chebyshev polynomials of first up to fourth kind. The limit $\alpha\to\infty$ leads back to the known Hermite polynomials orthogonal in the entire complex plane. When the ellipse degenerates to a circle we obtain the weight function and monomials known from the determinantal point process of the ensemble of truncated unitary random matrices. - Open Access
Universal microscopic correlation functions for products of truncated unitary matrices
We investigate the spectral properties of the product of $M$ complex non-Hermitian random matrices that are obtained by removing $L$ rows and columns of larger unitary random matrices uniformly distributed on the group ${\rm U}(N+L)$. Such matrices are called truncated unitary matrices or random contractions. We first derive the joint probability distribution for the eigenvalues of the product matrix for fixed $N,\ L$, and $M$, given by a standard determinantal point process in the complex plane. The weight however is non-standard and can be expressed in terms of the Meijer G-function. The explicit knowledge of all eigenvalue correlation functions and the corresponding kernel allows us to take various large $N$ (and $L$) limits at fixed $M$. At strong non-unitarity, with $L/N$ finite, the eigenvalues condense on a domain inside the unit circle. At the edge and in the bulk we find the same universal microscopic kernel as for a single complex non-Hermitian matrix from the Ginibre ensemble. At the origin we find the same new universality classes labelled by $M$ as for the product of $M$ matrices from the Ginibre ensemble. Keeping a fixed size of truncation, $L$, when $N$ goes to infinity leads to weak non-unitarity, with most eigenvalues on the unit circle as for unitary matrices. Here we find a new microscopic edge kernel that generalizes the known results for M=1. We briefly comment on the case when each product matrix results from a truncation of different size $L_j$.Open AccessUniversal microscopic correlation functions for products of truncated unitary matrices
We investigate the spectral properties of the product of $M$ complex non-Hermitian random matrices that are obtained by removing $L$ rows and columns of larger unitary random matrices uniformly distributed on the group ${\rm U}(N+L)$. Such matrices are called truncated unitary matrices or random contractions. We first derive the joint probability distribution for the eigenvalues of the product matrix for fixed $N,\ L$, and $M$, given by a standard determinantal point process in the complex plane. The weight however is non-standard and can be expressed in terms of the Meijer G-function. The explicit knowledge of all eigenvalue correlation functions and the corresponding kernel allows us to take various large $N$ (and $L$) limits at fixed $M$. At strong non-unitarity, with $L/N$ finite, the eigenvalues condense on a domain inside the unit circle. At the edge and in the bulk we find the same universal microscopic kernel as for a single complex non-Hermitian matrix from the Ginibre ensemble. At the origin we find the same new universality classes labelled by $M$ as for the product of $M$ matrices from the Ginibre ensemble. Keeping a fixed size of truncation, $L$, when $N$ goes to infinity leads to weak non-unitarity, with most eigenvalues on the unit circle as for unitary matrices. Here we find a new microscopic edge kernel that generalizes the known results for M=1. We briefly comment on the case when each product matrix results from a truncation of different size $L_j$. - 29 January 2013
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 46 (6) , 065003
Spectral density of complex networks with two species of nodes
- 29 January 2013
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 46 (6) , 065003
Spectral density of complex networks with two species of nodes
- Open Access
Parametric correlations versus fidelity decay: the symmetry breaking case
We derive fidelity decay and parametric energy correlations for random matrix ensembles where time--reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities can be established.
Open AccessParametric correlations versus fidelity decay: the symmetry breaking case
We derive fidelity decay and parametric energy correlations for random matrix ensembles where time--reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities can be established.
- Open Access
- 19 December 2011
- Published by American Physical Society (APS) in Physical Review E
- Vol. 84 (6) , 061133
Parametric correlations versus fidelity decay: The symmetry breaking case
We provide formulas for fidelity decay and parametric energy correlations for random matrix ensembles where time-reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities exists. Fidelity freeze is observed for systems with even and odd spin. DOI: http://dx.doi.org/10.1103/PhysRevE.84.061133 ©2011 American Physical Society
- 19 December 2011
- Published by American Physical Society (APS) in Physical Review E
- Vol. 84 (6) , 061133
Open AccessParametric correlations versus fidelity decay: The symmetry breaking case
We provide formulas for fidelity decay and parametric energy correlations for random matrix ensembles where time-reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities exists. Fidelity freeze is observed for systems with even and odd spin. DOI: http://dx.doi.org/10.1103/PhysRevE.84.061133 ©2011 American Physical Society
- 13 October 2011
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2011 (10) , 1-32
Random matrix theory for the Hermitian Wilson Dirac operator and the chGUE-GUE transition
- 13 October 2011
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2011 (10) , 1-32
Random matrix theory for the Hermitian Wilson Dirac operator and the chGUE-GUE transition
- 22 September 2007
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 129 (5-6) , 1137-1158
Pfaffian Expressions for Random Matrix Correlation Functions
- 22 September 2007
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 129 (5-6) , 1137-1158
Pfaffian Expressions for Random Matrix Correlation Functions