Using the minimum uncertainty state of quantum integrable system as initial state, the spatiotemporal evolution of the wave packet under the action of perturbed Hamiltonian is studied causally as in classical mechani...Using the minimum uncertainty state of quantum integrable system as initial state, the spatiotemporal evolution of the wave packet under the action of perturbed Hamiltonian is studied causally as in classical mechanics. Due to the existence of the avoided energy level crossing in the spectrum there exist nonlinear resonances between some pairs of neighboring components of the wave packet, the deterministic dynamical evolution becomes very complicated and appears to be chaotic. It is proposed to use expectation values for the whole set of basic dynamical variables and the corresponding spreading widths to describe the topological features concisely such that the quantum chaotic motion can be studied in contrast with the quantum regular motion and well characterized with the asymptotic behaviors. It has been demonstrated with numerical results that such a wave packet has indeed quantum behaviors of ergodicity as in corresponding classical case.展开更多
文摘Using the minimum uncertainty state of quantum integrable system as initial state, the spatiotemporal evolution of the wave packet under the action of perturbed Hamiltonian is studied causally as in classical mechanics. Due to the existence of the avoided energy level crossing in the spectrum there exist nonlinear resonances between some pairs of neighboring components of the wave packet, the deterministic dynamical evolution becomes very complicated and appears to be chaotic. It is proposed to use expectation values for the whole set of basic dynamical variables and the corresponding spreading widths to describe the topological features concisely such that the quantum chaotic motion can be studied in contrast with the quantum regular motion and well characterized with the asymptotic behaviors. It has been demonstrated with numerical results that such a wave packet has indeed quantum behaviors of ergodicity as in corresponding classical case.
基金上海市哲学社会科学规划课题"俄汉语义范畴的多维研究---二元对立视角的空间和时间范畴之对比"(2006BYY001)上海市浦江人才计划"俄汉语义范畴的多维研究与应用"(C类)(Shanghai Pujiang Program)+1 种基金教育部留学回国人员科研启动基金项目"汉俄语功能语法对比研究与应用"(The Project-sponsored by SRF for ROCSSEM)的阶段性成果