Semiclassical Theory for Universality in Quantum Chaos with Symmetry Crossover (2009)
Saito, Keiji, Nagao, Taro, Muller, Sebastian, Braun, Petr
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak...
The n-level spectral correlations for chaotic systems (2009)
Nagao, Taro, Müller, Sebastian
We study the $n$-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is...
Skew orthogonal polynomials and the partly symmetric real Ginibre ensemble (2008)
Forrester, Peter J., Nagao, Taro
The partly symmetric real Ginibre ensemble consists of matrices formed as linear combinations of real symmetric and real anti-symmetric Gaussian random matrices. Such matrices typically have both...
Spectral Density of Complex Networks with a Finite Mean Degree (2008)
In order to clarify the statistical features of complex networks, the spectral density of adjacency matrices has often been investigated. Adopting a static model introduced by Goh, Kahng and Kim, we...
Determinantal Correlations for Classical Projection Processes (2007)
Forrester, Peter J., Nagao, Taro
Recent applications in queuing theory and statistical mechanics have isolated the process formed by the eigenvalues of successive minors of the GUE. Analogous eigenvalue processes, formed in general...
Pfaffian Expressions for Random Matrix Correlation Functions (2007)
It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex...
Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2 (2007)
The spectral correlation of a chaotic system with spin 1/2 is universally described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the semiclassical limit. In semiclassical theory,...
Eigenvalue statistics of the real Ginibre ensemble (2007)
Forrester, Peter J., Nagao, Taro
The real Ginibre ensemble consists of random $N \times N$ matrices formed from i.i.d. standard Gaussian entries. By using the method of skew orthogonal polynomials, the general $n$-point correlations...
Spectral Density of Sparse Sample Covariance Matrices (2006)
Nagao, Taro, Tanaka, Toshiyuki
Applying the replica method of statistical mechanics, we evaluate the eigenvalue density of the large random matrix (sample covariance matrix) of the form $J = A^{\rm T} A$, where $A$ is an $M \times...
Semiclassical Theory for Parametric Correlation of Energy Levels (2006)
Nagao, Taro, Braun, Petr, Müller, Sebastian, Saito, Keiji, Heusler, Stefan, Haake, Fritz
Parametric energy-level correlation describes the response of the energy-level statistics to an external parameter such as the magnetic field. Using semiclassical periodic-orbit theory for a chaotic...
Correlation functions for random involutions (2006)
Forrester, Peter J., Nagao, Taro, Rains, Eric M.
Our interest is in the scaled joint distribution associated with k-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of...
Spectral Form Factor for Chaotic Dynamics in a Weak Magnetic Field (2005)
Using semiclassical periodic orbit theory for a chaotic system in a weak magnetic field, we obtain the form factor predicted by Pandey and Mehta's two matrix model up to the third order. The third...
Correlation functions for random involutions (2005)
Forrester, Peter J., Nagao, Taro, Rains, Eric M.
Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of...
Asymmetric Simple Exclusion Process and Modified Random Matrix Ensembles (2004)
Nagao, Taro, Sasamoto, Tomohiro
We study the fluctuation properties of the asymmetric simple exclusion process (ASEP) on an infinite one-dimensional lattice. When $N$ particles are initially situated in the negative region with a...
Katori, Makoto, Tanemura, Hideki, Nagao, Taro, Komatsuda, Naoaki
Spatially and temporally inhomogeneous evolution of one-dimensional vicious walkers with wall restriction is studied. We show that its continuum version is equivalent with a noncolliding system of...
Dynamical Correlations for Vicious Random Walk with a Wall (2003)
A one-dimensional system of nonintersecting Brownian particles is constructed as the diffusion scaling limit of Fisher's vicious random walk model. $N$ Brownian particles start from the origin at...
Infinite systems of non-colliding Brownian particles (2003)
Katori, Makoto, Nagao, Taro, Tanemura, Hideki
Non-colliding Brownian particles in one dimension is studied. $N$ Brownian particles start from the origin at time 0 and then they do not collide with each other until finite time $T$. We derive the...
Form Factor of a Quantum Graph in a Weak Magnetic Field (2002)
Using periodic orbit theory, we evaluate the form factor of a quantum graph to which a very weak magnetic field is applied. The first correction to the diagonal approximation describing the...
Dynamical Correlations for Circular Ensembles of Random Matrices (2002)
Nagao, Taro, Forrester, Peter J.
Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual...
Dynamical Correlations among Vicious Random Walkers (2002)
Nagao, Taro, Katori, Makoto, Tanemura, Hideki
Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin...
Vicious Random Walkers and a Discretization of Gaussian Random Matrix Ensembles (2001)
Nagao, Taro, Forrester, Peter J.
The vicious random walker problem on a one dimensional lattice is considered. Many walkers take simultaneous steps on the lattice and the configurations in which two of them arrive at the same site...
Chiral Lagrangians from lattice gauge theories in the strong coupling limit (2000)
Nagao, Taro, Nishigaki, Shinsuke M.
We derive nonlinear sigma models (chiral Lagrangians) over symmetric spaces U(n), U(2n)/Sp(2n), and U(2n)/O(2n) from U(N), O(N), and Sp(2N) lattice gauge theories coupled to n flavors of staggered...
Dynamical correlations among vicious random walkers
タネムラ, ヒデキ, 香取, 眞理, カトリ, マコト, Katori, Makoto, 永尾, 太郎, ナガオ, タロウ, ...
Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin...
Dynamical correlations among vicious random walkers
タネムラ, ヒデキ, 香取, 眞理, カトリ, マコト, Katori, Makoto, 永尾, 太郎, ナガオ, タロウ, ...
Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin...
Dynamical correlations among vicious random walkers
タネムラ, ヒデキ, 香取, 眞理, カトリ, マコト, Katori, Makoto, 永尾, 太郎, ナガオ, タロウ, ...
Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin...