1999/07/31 by Dae-Yup Song · 2 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.1103/physreva.61.024102
published as Phys.Rev.A61:024102,2000 · 11 pages, no figure, Phys. Rev. A (in press, as a Brief Reprt) An equality added in Eq.(16)
arxiv created 1999/10/20 · openalex publication_date 2000/01/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a time-dependent \ensuremathτ-periodic harmonic oscillator of two linearly independent homogeneous solutions of the classical equation of motion that are both bounded over time (stable), it is shown that there is a representation of states that are cyclic up to multiplicative constants under \ensuremathτ evolution or 2\ensuremathτ evolution depending on the model. The set of the wave functions is complete. Berry's phase, which could depend on the choice of representation, can be defined under the \ensuremathτ or 2\ensuremathτ evolution in this representation. If a homogeneous solution diverges as time goes to infinity, it is shown that such a Berry phase cannot be defined in any representation considered. Berry's phase for the driven harmonic oscillator is also considered. For the cases where Berry's phase can be defined, the phase is given in terms of solutions of the classical equation of motion.