<論文・報告>A review on so-called "principle of equal distance at the Kamo-gawa River"

Abstract

It is known that different geometrical structures of a phase space in a classical system (for example, "islands" indicating periodicity and chaotic "seas") correspond to different statistical properties of energy-level spacing in a quantum system. Characteristics of level repulsions and attractions are reflected in a functional form of probability distribution functions of level spacing. Such spacing statistics are also shown in human behavior. It is often said that couples sit evenly spaced apart along the Kamo-gawa River, which is a first-class river in the Yodo-gawa River System that flows through Kyoto City, Kyoto Prefecture. Statistics of such couple spacing are analyzed by actual measured values. Not only sitting couple spacing, but also walker, runner, and bicycle traveler spacing, is considered.

古典系の相空間の幾何学的構造(周期性を表す「島」やカオスの「海」)が対応する量子系のエネルギー準位の統計性に反映されることが知られている. エネルギー準位が反発したり, 引き合ったりした結果, エネルギー準位の間隔の分布関数にその特徴が現れる. このような間隔の分布については, 人間の行動にも表れる. 鴨川に腰掛けるカップルの間隔が等間隔になるという「法則」が知られているが, 鴨川のカップル間隔に関する統計性を求める. 座っているカップルのみならず, 歩く人, 走る人, 自転車の間隔についても議論したい.