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Negative Energy Ground States for the L2-Critical NLSE on Metric Graphs
We investigate the existence of ground states with prescribed mass for the focusing nonlinear Schrödinger equation with L2-critical power nonlinearity on noncompact quantum graphs. We prove that,Expand
Variational properties and orbital stability of standing waves for NLS equation on a star graph
We study standing waves for a model of nonlinear Schr\"odinger equation on a graph. The graph is obtained joining $N$ halflines at a vertex, i.e. it is a star graph. At the vertex an interactionExpand
Rigorous Derivation of the Cubic NLS in Dimension One
We derive rigorously the one-dimensional cubic nonlinear Schrödinger equation from a many-body quantum dynamics. The interaction potential is rescaled through a weak-coupling limit together with aExpand
Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy
On a star graph made of $N \geq 3$ halflines (edges) we consider a Schrodinger equation with a subcritical power-type nonlinearity and an attractive delta interaction located at the vertex. FromExpand
NLS ground states on graphs
We investigate the existence of ground states for the subcritical NLS energy on metric graphs. In particular, we find out a topological assumption that guarantees the nonexistence of ground states,Expand
A Class of Nonlinear Schro dinger Equations with Concentrated Nonlinearity
  • R. Adami
  • Mathematics, Physics
  • 20 February 2001
Abstract We consider the nonlinear Schrodinger equation in dimension one with a nonlinearity concentrated in a finite number of points. Detailed results on the local existence of the solution inExpand
On the Aharonov–Bohm Hamiltonian
Using the theory of self-adjoint extensions, we construct all the possible Hamiltonians describing the nonrelativistic Aharonov–Bohm effect. In general, the resulting Hamiltonians are notExpand
Stability and Symmetry-Breaking Bifurcation for the Ground States of a NLS with a δ′ Interaction
We determine and study the ground states of a focusing Schrödinger equation in dimension one with a power nonlinearity |ψ|2μψ and a strong inhomogeneity represented by a singular point perturbation,Expand
Threshold phenomena and existence results for NLS ground states on graphs
We investigate the existence of ground states of prescribed mass, for the nonlinear Schroedinger energy on a noncompact metric graph G. While in some cases the topology of G may rule out or, on theExpand
Controllability of the Schrödinger Equation via Intersection of Eigenvalues
  • R. Adami, U. Boscain
  • Mathematics
  • Proceedings of the 44th IEEE Conference on…
  • 12 December 2005
We introduce two models of controlled infinite dimensional quantum system whose Hamiltonian operator has a purely discrete spectrum. For any couple of eigenstates we construct a path in the space ofExpand