Study on classical and quantum models on graphs

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540116
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Yokohama National University
• Principal Investigator: KONNO Norio 横浜国立大学, 工学(系)研究科(研究院), 教授 (80205575)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 量子ウォーク / 複雑ネットワーク / アダマールウォーク / 定常測度 / 極限定理 / 局在化

Outline of Final Research Achievements

We obtained stationary measures, time-averaged limit measures, and weak limit measures for quantum walks on various graphs. For examples, we got a formula of characteristic polynomials of the unitary matrix determines the quantum walk on graphs by the weighted zeta function. We obtained stationary measures of two-state quantum walk on the line, in particular, a non-uniform stationary measure for the Hadamard walk. Moreover we got stationary measures, time-averaged limit measures, and weak limit measures for a class of quantum walks with one defect and clarified the localization. We analyzed localization of quantum walks on glued trees and spidernets.

Free Research Field

数学一般(含確率論・統計数学)