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Register a new userThe semiclassical limit on a star-graph with Kirchhoff conditions
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Added by
Claudio Cacciapuoti
Publication date
2020
fields
Physics
and research's language is
English
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We consider the dynamics of a quantum particle of mass $m$ on a $n$-edges star-graph with Hamiltonian $H_K=-(2m)^{-1}hbar^2 Delta$ 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 Kreu{i}ns 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 $(H_K,H_{D}^{oplus})$, where $H_{D}^{oplus}$ is the free Hamiltonian with Dirichlet conditions in the vertex.
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