Mathematics of Quantum-Classical correspondence and the Arcsine law

2017 Fiscal Year Final Research Report

• Project/Area Number: 26870696
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical informatics; Mathematical physics/Fundamental condensed matter physics
• Research Institution: Nagahama Institute of Bio-Science and Technology
• Principal Investigator: Saigo Hayato 長浜バイオ大学, バイオサイエンス学部, 准教授 (80615154)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 量子古典対応 / 逆正弦法則 / 直交多項式 / 量子ウォーク / ヘッケ環

Outline of Final Research Achievements

The idea of "quantum classical correspondence", which unifies the quantum physics and the world of classical physics, is reformulated in the framework of a branch of modern mathematics called "quantum probability theory". The universal roles played by "the Arcsine law" in the realm of mathematical sciences are clarified. For instance, the behavior and structures of important mathematical objects such as "orthogonal polynomials", "quantum walks" and "Hecke rings" are analysed in terms of the Arcsine law from the viewpoint of quantum probability.

Free Research Field

数理物理・量子確率論