We consider time-dependent Schrodinger equations in one dimension with double-well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest eigenvalues, then, in the semiclassical limit, we show that the reduction of the time-dependent equation to a 2-mode equation gives the dominant term of the solution with a precise estimate of the error. By means of this stability result we are able to prove the absence of the beating motion for large enough nonlinearity.

Nonlinear time-dependent one-dimensional Schrodinger equation with double-well potential / Sacchetti, Andrea. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 35:(2004), pp. 1160-1176. [10.1137/S0036141002415438]

Nonlinear time-dependent one-dimensional Schrodinger equation with double-well potential

SACCHETTI, Andrea
2004-01-01

Abstract

We consider time-dependent Schrodinger equations in one dimension with double-well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest eigenvalues, then, in the semiclassical limit, we show that the reduction of the time-dependent equation to a 2-mode equation gives the dominant term of the solution with a precise estimate of the error. By means of this stability result we are able to prove the absence of the beating motion for large enough nonlinearity.
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Nonlinear time-dependent one-dimensional Schrodinger equation with double-well potential / Sacchetti, Andrea. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 35:(2004), pp. 1160-1176. [10.1137/S0036141002415438]
Sacchetti, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/306410
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