数理物理セミナー: Convergence Rates for Homogeneous Unitary Quantum Walks on the Integers (Pascal Mittenbühler 氏)

Time： 17:00-18:00

Place：理学部3号館 3-210

Speaker：Pascal Mittenbühler 氏（Paderborn University）

Title：Convergence Rates for Homogeneous Unitary Quantum Walks on the Integers

Abstract：We analyze the long-time behavior of discrete-time quantum walks on the integers with space- and time-homogeneous unitary evolution. Using a matrix-function representation, we study the pointwise convergence of characteristic functions under ballistic rescaling. By combining explicit bounds on this convergence with a modified version of a classical estimate due to Zolotarev, we obtain rates of convergence for the associated position distributions, measured in terms of the Lévy metric. Our results apply to the general class of unitary evolutions whose Fourier transforms are analytic, and provide quantitative insight into how fast the walk approaches its asymptotic distribution. The question of whether our bounds are optimal remains open.

Organizer：宮尾 忠宏（北海道大学）