偏微分方程式セミナー: Connection between discrete- and continuous-time quantum walks via the Heun equation

開催日時
2012年   6月 18日 16時 30分 ~ 2012年   6月 18日 17時 30分
場所
北大理学部3号館309室
講演者
町田拓也(明治大学)
 
Quantum walks, which are quantum counterparts of classical random walks,
have been investigated recently.
The limit theorems of discrete- and continuous-time quantum walks on the
line have been intensively studied.
We show a relationship among limit distributions of quantum walks, Heun
differential equations and Gauss differential equations.
Moreover, using both differential equations, we discuss connection between

discrete- and continuous-time quantum walks via the confluent Heun
equation.
Taking suitable limit, we can transform a Heun equation obtained from the
limit density function of the discrete-time quantum walk to a Gauss
equation
given by that of the continuous-time quantum walk.
These results are based on [1].

[1] Konno, N., Machida, T., Wakasa, T.: The Heun differential equation and

the Gauss differential equation related to quantum walks, Yokohama
Mathematical Journal (in press), arXiv:1109.2662.

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