We consider time-dependent Schrodinger equations with a double well potential and an external nonlinear, both local and non-local, perturbation. In the semiclassical limit, the finite dimensional eigenspace associated to the lowest eigenvalues of the linear operator is almost invariant for times of the order of the beating period and the dominant term of the wavefunction is given by means of the solutions of a finite dimensional dynamical system. In the case of local nonlinear perturbation, we assume the spatial dimension d=1 or d=2.
Nonlinear double-well Schrodinger equations in the semiclassical limit / Sacchetti, Andrea. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 119:(2005), pp. 1347-1382. [10.1007/s10955-005-3766-x]
Nonlinear double-well Schrodinger equations in the semiclassical limit
SACCHETTI, Andrea
2005
Abstract
We consider time-dependent Schrodinger equations with a double well potential and an external nonlinear, both local and non-local, perturbation. In the semiclassical limit, the finite dimensional eigenspace associated to the lowest eigenvalues of the linear operator is almost invariant for times of the order of the beating period and the dominant term of the wavefunction is given by means of the solutions of a finite dimensional dynamical system. In the case of local nonlinear perturbation, we assume the spatial dimension d=1 or d=2.Pubblicazioni consigliate
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