On a Linear Chaotic Quantum Harmonic Oscillator
  We show that a linear quantum harmonic oscillator is chaotic in the sense of Li-Yorke. We also prove that the weighted backward shift map, used as an infinite dimensional linear chaos model, in a separable Hilbert space is chaotic in the sense of Li-Yorke, in addition to being chaotic in the sense of Devaney. 
Jinqiao Duan, Xin-Chu Fu, Pei-De Liu, and Anthony Manning