 04235 Andrea Sacchetti
 Nonlinear double well Schrodinger equations in the semiclassical limit
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Jul 29, 04

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Abstract. We consider timedependent Schrodinger equations with a double well potential and an external nonlinear, both local and nonlocal, 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
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