PDE seminar:Connection between discrete- and continuous-time quantum walks via the Heun equation

Date
2012-6-18 16:30 - 2012-6-18 17:30
Place
Faculty of Science Building #3 Room 309
Speaker/Organizer
Takuya Machida (Meiji Univ.)
 
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.