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math.AP2024
Intertwining operators beyond the Stark Effect
Luca Fanelli, Xiaoyan Su, Ying Wang +2
The main mathematical manifestation of the Stark effect in quantum mechanics is the shift and the formation of clusters of eigenvalues when a spherical Hamiltonian is perturbed by…
math.AP2024
Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
Miguel Á. Alejo, Lucrezia Cossetti, Luca Fanelli +2
We consider the subcritical nonlinear Schrödinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximat…
math.AP2023
Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials
Lucrezia Cossetti, Luca Fanelli, David Krejcirik
We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under whi…