Destruction of the Beating Effect¶for a Non-Linear Schrödinger Equation

Simulation of resonant tunneling heterostructures: numerical comparison of a complete Schrödinger-Poisson system and a reduced nonlinear model

“…Thus the time dependent electrostatic description of the charge effect is relevant (no electomagnetic model is required). Note that the damping is increasing when the nonlinear effects are stronger, in agreement with what is observed in some other models studied for example in [20]) where the nonlinearity kills the beating effect after reaching a critical strength. Such a theoretical study would be valuable here but requires some heavy mathematical techniques.…”

Nonlinear time-dependent Schr�dinger equations: the Gross-Pitaevskii equation with double-well potential

“…A similar analysis has been recently performed in [6] where the nonlinear perturbation is given by ψ, gψ gψ and g(x) is a given symmetric function. We emphasize that in such a case the crucial a priori estimate of the non-linear term immediately follows from the conservation of the norm of the wave-function.…”

“…REMARK 3. We underline that a similar criterion has been recently given by [6] for a class of double-well Schrödinger equations under the effect of a nonlinear perturbation of the form ψ, gψ gψ where g is a given symmetric function. Here, we extend the validity of such a criterion to the Gross-Pitaevskii equation.…”

Interaction of Coherent States for Hartree Equations

“…In [23,38,39], a semiclassical regime is studied in the presence of an external potential and a nonlinearity. The potential is a double well potential, and the associated Hamiltonian has two eigenfunctions.…”