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Title: Commutability between the Semiclassical and Adiabatic Limits

Abstract

We study the adiabatic limit and the semiclassical limit with a second-quantized two-mode model of a many-boson interacting system. When its mean-field interaction is small, these two limits are commutable. However, when the interaction is strong and over a critical value, the two limits become incommutable. This change of commutability is associated with a topological change in the structure of the energy bands. These results reveal that nonlinear mean-field theories, such as Gross-Pitaevskii equations for Bose-Einstein condensates, can be invalid in the adiabatic limit.

Authors:
 [1];  [2]
  1. Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080 (China)
  2. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China)
Publication Date:
OSTI Identifier:
20775029
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 96; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevLett.96.020405; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; BOSONS; EQUATIONS; MEAN-FIELD THEORY; NONLINEAR PROBLEMS; SEMICLASSICAL APPROXIMATION; TOPOLOGY

Citation Formats

Wu Biao, and Liu Jie. Commutability between the Semiclassical and Adiabatic Limits. United States: N. p., 2006. Web. doi:10.1103/PhysRevLett.96.020405.
Wu Biao, & Liu Jie. Commutability between the Semiclassical and Adiabatic Limits. United States. doi:10.1103/PhysRevLett.96.020405.
Wu Biao, and Liu Jie. Fri . "Commutability between the Semiclassical and Adiabatic Limits". United States. doi:10.1103/PhysRevLett.96.020405.
@article{osti_20775029,
title = {Commutability between the Semiclassical and Adiabatic Limits},
author = {Wu Biao and Liu Jie},
abstractNote = {We study the adiabatic limit and the semiclassical limit with a second-quantized two-mode model of a many-boson interacting system. When its mean-field interaction is small, these two limits are commutable. However, when the interaction is strong and over a critical value, the two limits become incommutable. This change of commutability is associated with a topological change in the structure of the energy bands. These results reveal that nonlinear mean-field theories, such as Gross-Pitaevskii equations for Bose-Einstein condensates, can be invalid in the adiabatic limit.},
doi = {10.1103/PhysRevLett.96.020405},
journal = {Physical Review Letters},
number = 2,
volume = 96,
place = {United States},
year = {Fri Jan 20 00:00:00 EST 2006},
month = {Fri Jan 20 00:00:00 EST 2006}
}