In this paper we consider time dependent Schrödinger linear PDEs of the form i∂ t ψ= L (t)
ψ, where L (t) is a continuous family of self-adjoint operators. We give conditions for well …

We prove an abstract theorem giving a〈 t〉 ϵ bound (for all ϵ> 0) on the growth of the
Sobolev norms in linear Schrödinger equations of the form i ψ= H0ψ+ V (t) ψ as t→∞. The …

We investigate a group B• that includes Artin's braid group B∞ and Thompson's group F.
The elements of B• are represented by braids diagrams in which the distances between the …

Growth of Sobolev norms for unbounded perturbations of the Schrödinger equation on flat tori -
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We give a new proof of a theorem of Bourgain 4 asserting that solutions of linear
Schrödinger equations on the torus, with smooth time-dependent potential, have Sobolev …

It has been known for some time that solutions of linear Schrödinger operators on the torus,
with bounded, smooth, time dependent (order zero pseudo-differential) potential, have …

We consider a quantum particle in a periodic structure submitted to a constant external
electromotive force. The periodic background is given by a smooth potential plus singular …

We improve Delort's method to show that solutions of linear Schrödinger equations with a
time dependent Gevrey potential on the torus, have at most logarithmically growing Sobolev …

The main motivation of this article is to derive sufficient conditions for dynamical stability of
periodically driven quantum systems described by a Hamiltonian H (t), ie conditions under …

We consider quantum Hamiltonians of the form H (t)= H+ V (t) where the spectrum of H is
semibounded and discrete, and the eigenvalues behave as E n∼ n α, with 0< α< 1. In …