2014/12/01 by Akira Shudo, Yasutaka Hanada, Teruaki Okushima +1 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Instanton #Integrable system #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Quantum #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum tunnelling #Transition of state #nlin.CD
paper · pdf · doi:10.1209/0295-5075/108/50004
published as Europhysics Letters 108 (2014) 50004 · 6 pages, 4 figures
openalex publication_date 2014/12/01 · arxiv created 2015/03/02 · arxiv updated 2015/03/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The instanton-noninstanton (I-NI) transition in the tunneling process, which has been numerically observed in classically nonintegrable quantum maps, can be described by a perturbation theory based on an integrable Hamiltonian renormalized so as to incorporate the integrable part of the map. The renormalized perturbation theory is successfully applied to the two quantum maps, the Hénon and standard maps. In spite of the different nature of tunneling in the two systems, the I-NI transition exhibits very common characteristics. In particular, the manifestation of I-NI transition is obviously explained by a remarkable quenching of the renormalized transition matrix element. The enhancement of tunneling probability after the transition can be understood as a sudden change of the tunneling mechanism from the instanton to quite a different mechanism supported by classical flows just outside of the stable-unstable manifolds of the saddle on the top of the potential barrier.