2008/06/30 by Wenhua Hai, Qianquan Zhu, Shiguang Rong
Physics and Astronomy · #Amplitude #Bose–Einstein condensate #Chaotic #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Harmonic #Mechanics #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Shock (circulatory) #Shock front #Shock wave #Strong Light-Matter Interactions #cond-mat.other #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physreva.79.023603
published as PHYSICAL REVIEW A 79, 023603 (2009) · 5 pages, 1 figures
openalex publication_date 2009/02/03 · arxiv created 2009/02/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is demonstrated that the well-known Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate (BEC) driven by the time-periodic harmonic or inverted-harmonic potential. A formally exact solution of the time-dependent Gross-Pitaevskii equation is constructed, which describes the matter shock waves with chaotic or periodic amplitudes and phases. When the periodic driving is switched off and the number of condensed atoms is conserved, we obtained the exact stationary states and nonstationary states. The former contains the stable ``nonpropagated'' shock wave, and in the latter the shock wave alternately collapses and grows for the harmonic trapping or propagates with exponentially increased shock-front speed for the antitrapping. It is revealed that the existence of chaos plays a role for suppressing the blast of matter wave. The results suggest a method for preparing the exponentially accelerated BEC shock waves or the stable stationary states.