We consider the dynamics of a quantum particle of mass m on a n-edges star-graph with Hamiltonian HK=−(2m)−1ℏ2Δ and Kirchhoff conditions in the vertex. We describe the semiclassical limit of the quantum evolution of an initial state supported on one of the edges and close to a Gaussian coherent state. We define the limiting classical dynamics through a Liouville operator on the graph, obtained by means of Kreĭn’s theory of singular perturbations of self-adjoint operators. For the same class of initial states, we study the semiclassical limit of the wave and scattering operators for the couple (HK,H⊕D), where H⊕D is the Hamiltonian with Dirichlet conditions in the vertex.

Cacciapuoti, C., Fermi, D., & Posilicano, A. (2021). The semiclassical limit on a star-graph with Kirchhoff conditions, 11(2) [10.1007/s13324-020-00455-3].

The semiclassical limit on a star-graph with Kirchhoff conditions

Cacciapuoti C.;Fermi D.
;
2021

Abstract

We consider the dynamics of a quantum particle of mass m on a n-edges star-graph with Hamiltonian HK=−(2m)−1ℏ2Δ and Kirchhoff conditions in the vertex. We describe the semiclassical limit of the quantum evolution of an initial state supported on one of the edges and close to a Gaussian coherent state. We define the limiting classical dynamics through a Liouville operator on the graph, obtained by means of Kreĭn’s theory of singular perturbations of self-adjoint operators. For the same class of initial states, we study the semiclassical limit of the wave and scattering operators for the couple (HK,H⊕D), where H⊕D is the Hamiltonian with Dirichlet conditions in the vertex.
Cacciapuoti, C., Fermi, D., & Posilicano, A. (2021). The semiclassical limit on a star-graph with Kirchhoff conditions, 11(2) [10.1007/s13324-020-00455-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/413924
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