Stability of spectral eigenspaces in nonlinear Schrodinger equations

2006/08/03 by Bambusi, Dario, Sacchetti, Andrea
#35Bxx (Primary) #35K55 (Secondary) #35Q40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.math-ph/0608010

Abstract

We consider the time-dependent non linear Schrodinger equations with a double well potential in dimensions d =1 and d=2. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest two eigenvalues of the linear operator is almost invariant for any time.

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