78 citations · 618 across the 47 of their papers we have counts for
48 papers
Quantum resonances and analysis of the survival amplitude in the nonlinear Winter's model
Andrea Sacchetti
In this paper we show that the typical effects of quantum resonances, namely, the exponential-type decay of the survival amplitude, continue to exist even when a nonlinear perturba…
Perturbation theory for nonlinear Schrodinger equations
Andrea Sacchetti
Treating the nonlinear term of the Gross-Pitaevskii nonlinear Schrodinger equation as a perturbation of an isolated discrete eigenvalue of the linear problem one obtains a Rayleigh…
Enhancement of the Zakharov-Glassey's method for Blow-Up in nonlinear Schroedinger equations
Andrea Sacchetti
In this paper we give a sharper condition for the blow-up of the solution to a nonlinear Schroedinger equation with free/Stark/quadratic potential by improving the well known Zakha…
Neural Networks to solve Partial Differential Equations: a Comparison with Finite Elements
Andrea Sacchetti, Benjamin Bachmann, Kaspar Löffel +2
We compare the Finite Element Method (FEM) simulation of a standard Partial Differential Equation thermal problem of a plate with a hole with a Neural Network (NN) simulation. The…
Spectral splitting method for nonlinear Schrödinger equations with quadratic potential
Andrea Sacchetti
In this paper we propose a modified Lie-type spectral splitting approximation where the external potential is of quadratic type. It is proved that we can approximate the solution t…
Quantum forced oscillator via Wigner transform
Andrea Sacchetti
In this paper we review the basic results concerning the Wigner transform and then we completely solve the quantum forced harmonic/inverted oscillator in such a framework; eventual…