Trajectory-based understanding of the quantum–classical transition for barrier scattering

Journal Article · Fri Jun 15 04:00:00 EDT 2018 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2018.04.017· OSTI ID:22848347

Chou, Chia-Chun ^[1]

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1. Department of Chemistry, National Tsing Hua University, Hsinchu, 30013, Taiwan (China)

The quantum–classical transition of wave packet barrier scattering is investigated using a hydrodynamic description in the framework of a nonlinear Schrödinger equation. The nonlinear equation provides a continuous description for the quantum–classical transition of physical systems by introducing a degree of quantumness. Based on the transition equation, the transition trajectory formalism is developed to establish the connection between classical and quantum trajectories. The quantum–classical transition is then analyzed for the scattering of a Gaussian wave packet from an Eckart barrier and the decay of a metastable state. Computational results for the evolution of the wave packet and the transmission probabilities indicate that classical results are recovered when the degree of quantumness tends to zero. Classical trajectories are in excellent agreement with the transition trajectories in the classical limit, except in some regions where transition trajectories cannot cross because of the single-valuedness of the transition wave function. As the computational results demonstrate, the process that the Planck constant tends to zero is equivalent to the gradual removal of quantum effects originating from the quantum potential. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet barrier scattering.

• OSTI ID: 22848347
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 393; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HYDRODYNAMICS
METASTABLE STATES
NONLINEAR PROBLEMS
SCATTERING
SCHROEDINGER EQUATION
WAVE FUNCTIONS
WAVE PACKETS