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Volumn 66, Issue 5, 2002, Pages

Loading a Bose-Einstein condensate onto an optical lattice: An application of optimal control theory to the nonlinear Schrödinger equation

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; BOUNDARY CONDITIONS; HAMILTONIANS; INTEGRAL EQUATIONS; ITERATIVE METHODS; LINEAR EQUATIONS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0036878066     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (116)

References (18)
  • 8
    • 0013101937 scopus 로고    scopus 로고
    • note
    • Here and throughout the following, vector treatment of the appropriate variables is assumed, although all vector notations are omitted to avoid congestion. Multiplication of vector variables is therefore to be understood as a dot product. An indexed notation of vector components will be used only when unavoidalbe for clarity, and summation convention will then be implied.
  • 10
    • 0013105122 scopus 로고    scopus 로고
    • note
    • In the derivation below, the following delicate point should be noted: R (t, ψ, u) is, by definition, a function of three variables, whereas H(t,ψ,u,p) is a function of an additional argument p = ∂φ/∂ψ. In other words, although p depends on ψ with respect to R, this is not the case with respect to H where ψ and p are to be taken as independent variables. I Eq. (17), we wish to vary R with respect to ψ, which means H must be varied in both ψ and p; ∂R/∂ψ↔{(∂p/∂ψ)∂/∂p + ∂/∂ψ}H.
  • 11
    • 85088491721 scopus 로고    scopus 로고
    • note
    • ψ0 is translated to a simple time derivative of χ(t).
  • 14
    • 85088490942 scopus 로고    scopus 로고
    • note
    • T)=<>, where B is some target state. In this form the equivalence to the linear case becomes self-evident.
  • 15
    • 0013053838 scopus 로고    scopus 로고
    • note
    • -1∂H/∂u to be a correction to the old field instead of an entirely new choice.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.