The quantum‐classical correspondence for the degree of freedom in 2D irregular sound fields

Abstract

AbstractIn the area of research on quantum chaos, the correspondence between the quantum and classical theories on the chaos is a problem. In the billiard problem of a stadium type in a classical system (to be replaced with the acoustic line tracing the acoustics), it is known that the acoustic line locus exhibits a chaotic behavior. However, no chaos exists in the wave phenomena in a quantum system as a linear wave field. Where in the linear wave field a chaotic behavior exists and how the linear wave field is related to the chaotic nature of the classical system have been research topics. The objective of the present research is to search the correspondence between the classical and quantum theories on the chaos from the point of view of indoor acoustics. The authors define semistadium boundaries with higher‐order curves of more than second order and calculate the degrees of freedom in the wave system and classical system. From the point of view of degrees of freedom in the system, the correspondence is analyzed on the chaos between the wave and classical theories. It is found that the correspondence between the chaotic nature of the acoustic line propagation and the wave nature depends on the degrees of freedom of the system. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(3): 61–68, 2002