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Title: Trajectory description of the quantum–classical transition for wave packet interference

Abstract

The quantum–classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum–classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum–classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow the main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum–classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightfulmore » trajectory interpretation for the quantum–classical transition of wave packet interference.« less

Authors:
Publication Date:
OSTI Identifier:
22560342
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 371; Journal Issue: Complete; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFRACTION; HAMILTON-JACOBI EQUATIONS; INTERFERENCE; NONLINEAR PROBLEMS; PROBABILITY; SCHROEDINGER EQUATION; TIME DEPENDENCE; VELOCITY; WAVE FUNCTIONS; WAVE PACKETS

Citation Formats

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw. Trajectory description of the quantum–classical transition for wave packet interference. United States: N. p., 2016. Web. doi:10.1016/J.AOP.2016.06.001.
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw. Trajectory description of the quantum–classical transition for wave packet interference. United States. doi:10.1016/J.AOP.2016.06.001.
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw. 2016. "Trajectory description of the quantum–classical transition for wave packet interference". United States. doi:10.1016/J.AOP.2016.06.001.
@article{osti_22560342,
title = {Trajectory description of the quantum–classical transition for wave packet interference},
author = {Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw},
abstractNote = {The quantum–classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum–classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum–classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow the main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum–classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet interference.},
doi = {10.1016/J.AOP.2016.06.001},
journal = {Annals of Physics},
number = Complete,
volume = 371,
place = {United States},
year = 2016,
month = 8
}
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