Characteristics of the Wave Function of Coupled Oscillators in Semiquantum Chaos

TL;DR

This paper investigates the wave functions of coupled oscillators in semiquantum chaos, revealing spectral and correlation features that distinguish regular from chaotic states, using adiabatic invariants and the Born-Oppenheimer approximation.

Contribution

It introduces a novel approach to characterize semiquantum chaos through wave function analysis, providing new insights into quantum state distinctions.

Findings

Fourier spectra differ between regular and chaotic states

Correlation functions reveal characteristic patterns in chaos

Wave functions exhibit unique features in semiquantum chaos

Abstract

Using the method of adiabatic invariants and the Born-Oppenheimer approximation, we have successfully got the excited-state wave functions for a pair of coupled oscillators in the so-called \textit{semiquantum chaos}. Some interesting characteristics in the \textit{Fourier spectra} of the wave functions and its \textit{Correlation Functions} in the regular and chaos states have been found, which offers a new way to distinguish the regular and chaotic states in quantum system.