Wigner Function Flow in Generalized Quantum Harmonic Oscillators Popo Yang ^{1*}, Shin-Tza Wu^{2}, Ray-Kuang Lee^{1,3,4}^{1}Department of Physics, National Tsing Hua University, Hsinchu, Taiwan^{2}Department of Physics, National Chung Cheng University, Chiayi, Taiwan^{3}Institute of Photonics, National Tsing Hua University, Hsinchu, Taiwan^{4}Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan* Presenter:Popo Yang, email:popoycr@gmail.com We develop a continuity equation for Wigner function flow and calculate the corresponding circulation values, for generalized quantum harmonic oscillators with parity-time (PT) symmetry or with parametric optical process. For the PT-symmetric non-Hermitian Hamiltonian, we reveal how a PT -symmetry breaking manifests itself in the phase-space representation through the circulation values of Wigner function flows; while for the optical parametric oscillators (OPO), how the vacuum states evolves into squeezed states and interference inside Schrodinger cat states are revisited through the Wigner function flow.
Keywords: Wigner distribution function, Wigner flow, PT symmetry |