21 citations
8 papers
Jarlskog's Parametrization of Unitary Matrices and Qudit Theory
Kazuyuki Fujii, Kunio Funahashi, Takayuki Kobayashi
In the paper (math-ph/0504049) Jarlskog gave an interesting simple parametrization to unitary matrices, which was essentially the canonical coordinate of the second kind in the Lie…
Power-law tails in nonstationary stochastic processes with asymmetrically multiplicative interactions
Akihiro Fujihara, Toshiya Ohtsuki, Hiroshi Yamamoto
We consider stochastic processes where randomly chosen particles with positive quantities x, y (> 0) interact and exchange the quantities asymmetrically by the rule x' = c{(1-a) x…
Comment on "A Recursive Parametrisation of Unitary Matrices"
Kazuyuki Fujii
In this note we make a comment on the paper by Jarlskog (math-ph/0504049) in which she gave a parametrisation to unitary matrices. Namely, we show that her recursive method is esse…
From Quantum Optics to Non-Commutative Geometry : A Non-Commutative Version of the Hopf Bundle, Veronese Mapping and Spin Representation
Kazuyuki Fujii
In this paper we construct a non-commutative version of the Hopf bundle by making use of Jaynes-Commings model and so-called Quantum Diagonalization Method. The bundle has a kind o…
Jaynes-Cummings Model and a Non-Commutative "Geometry" : A Few Problems Noted
Kazuyuki Fujii
In this paper we point out that the Jaynes-Cummings model without taking a renonance conditon gives a non-commutative version of the simple spin model (including the parameters …
The Heun equation and the Calogero-Moser-Sutherland system IV: the Hermite-Krichever Ansatz
Kouichi Takemura
We develop a theory for the Hermite-Krichever Ansatz on the Heun equation. As a byproduct, we find formulae which reduce hyperelliptic integrals to elliptic ones.