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Title: Adiabatic Condition for Nonlinear Systems

Abstract

The adiabatic approximation is an important concept in quantum mechanics. In linear systems, the adiabatic condition is derived with the help of the instantaneous eigenvalues and eigenstates of the Hamiltonian, a procedure that breaks down in the presence of nonlinearity. Using an explicit example relevant to photoassociation of atoms into diatomic molecules, we demonstrate that the proper way to derive the adiabatic condition for nonlinear mean-field (or classical) systems is through a linearization procedure, using which an analytic adiabatic condition is obtained for the nonlinear model under study.

Authors:
 [1]; ;  [2];  [3]
  1. Department of Physics and Astronomy, and Rice Quantum Institute, Rice University, Houston, Texas 77251-1892 (United States)
  2. Department of Physics and Astronomy, Rowan University, Glassboro, New Jersey, 08028-1700 (United States)
  3. Key Laboratory of Optical and Magnetic Resonance Spectroscopy (Ministry of Education), Department of Physics, East China Normal University, Shanghai 200062 (China)
Publication Date:
OSTI Identifier:
20955409
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevLett.98.050406; (c) 2007 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; ADIABATIC APPROXIMATION; EIGENSTATES; EIGENVALUES; HAMILTONIANS; MEAN-FIELD THEORY; NONLINEAR PROBLEMS; QUANTUM MECHANICS

Citation Formats

Pu Han, Maenner, Peter, Ling, Hong Y., and Zhang Weiping. Adiabatic Condition for Nonlinear Systems. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.050406.
Pu Han, Maenner, Peter, Ling, Hong Y., & Zhang Weiping. Adiabatic Condition for Nonlinear Systems. United States. doi:10.1103/PHYSREVLETT.98.050406.
Pu Han, Maenner, Peter, Ling, Hong Y., and Zhang Weiping. Fri . "Adiabatic Condition for Nonlinear Systems". United States. doi:10.1103/PHYSREVLETT.98.050406.
@article{osti_20955409,
title = {Adiabatic Condition for Nonlinear Systems},
author = {Pu Han and Maenner, Peter and Ling, Hong Y. and Zhang Weiping},
abstractNote = {The adiabatic approximation is an important concept in quantum mechanics. In linear systems, the adiabatic condition is derived with the help of the instantaneous eigenvalues and eigenstates of the Hamiltonian, a procedure that breaks down in the presence of nonlinearity. Using an explicit example relevant to photoassociation of atoms into diatomic molecules, we demonstrate that the proper way to derive the adiabatic condition for nonlinear mean-field (or classical) systems is through a linearization procedure, using which an analytic adiabatic condition is obtained for the nonlinear model under study.},
doi = {10.1103/PHYSREVLETT.98.050406},
journal = {Physical Review Letters},
number = 5,
volume = 98,
place = {United States},
year = {Fri Feb 02 00:00:00 EST 2007},
month = {Fri Feb 02 00:00:00 EST 2007}
}