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.affiliation: Department of Physics and Astronomy, and Rice Quantum Institute, Rice University, Houston, Texas 77251-1892, USA.
authors.forename: Han
authors.initials: H
authors.lastname: Pu
authors.forename: Peter
authors.initials: P
authors.lastname: Maenner
authors.forename: Weiping
authors.initials: W
authors.lastname: Zhang
authors.forename: Hong Y
authors.initials: HY
authors.lastname: Ling