2003年8月
Vicious walks with a wall, noncolliding meanders, and chiral and Bogoliubov-de Gennes random matrices
PHYSICAL REVIEW E
- ,
- ,
- ,
- 巻
- 68
- 号
- 2
- 開始ページ
- p.021112
- 終了ページ
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1103/PhysRevE.68.021112
- 出版者・発行元
- AMER PHYSICAL SOC
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 stochastic processes called Brownian meanders. Here the Brownian meander is a temporally inhomogeneous process introduced by Yor as a transform of the Bessel process that is the motion of radial coordinate of the three-dimensional Brownian motion represented in spherical coordinates. It is proved that the spatial distribution of vicious walkers with a wall at the origin can be described by the eigenvalue statistics of Gaussian ensembles of Bogoliubov-de Gennes Hamiltonians of the mean-field theory of superconductivity, which have a particle-hole symmetry. We report that a time evolution of the present stochastic process is fully characterized by the change of symmetry classes from type C to type CI in the nonstandard classes of random matrix theory of Altland and Zirnbauer. The relation between the noncolliding systems of the generalized meanders of Yor, which are associated with the even-dimensional Bessel processes, and the chiral random matrix theory is also clarified.
- リンク情報
- ID情報
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- DOI : 10.1103/PhysRevE.68.021112
- ISSN : 1539-3755
- Web of Science ID : WOS:000185193900021