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. ANALYSIS AND MATHEMATICAL PHYSICS, 11(2) [10.1007/s13324-020-00455-3].
The semiclassical limit on a star-graph with Kirchhoff conditions
Cacciapuoti C.;Fermi D.
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2021-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
