Volume 57, Number 6, March 2002
|Page(s)||789 - 795|
|Published online||01 August 2002|
Classical integrability and quantum velocity fields
Department of Physics and Centre for Nonlinear
Studies Hong Kong Baptist University - Hong Kong, PRC
2 Department of Physics, University of Houston Houston TX 77204-5506, USA
3 Institute of Modern Physics, Southwest Jiaotong University Chengdu 610031, PRC
Accepted: 28 December 2001
We study a stationary velocity field, defined via the probability current density for an energy eigenstate of a quantum system, and its classical analog determined by the Hamilton-Jacobi equation. For classically integrable systems, the quantum-classical correspondence can be properly established by specifying constants of motion in addition to the Hamiltonian. For classically chaotic systems, the correspondence is broken down; the manifestation of classical chaos in the quantum domain is shown numerically to be the appearance of turbulence in the quantum velocity field.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 03.65.Bz – Foundations, theory of measurement, miscellaneous theories (including Aharonov-Bohm effect, Bell inequalities, Berry's phase) / 47.27.-i – Turbulent flows, convection, and heat transfer
© EDP Sciences, 2002
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