论文标题
具有Kirchhoff条件的星际纸的半经典限制
The semiclassical limit on a star-graph with Kirchhoff conditions
论文作者
论文摘要
我们考虑$ n $ m $的量子粒子在$ n $ edges star-graph上使用hamiltonian $ h_k = - （2m）^{ - 1} \ hbar^2Δ$和kirchhoff条件。我们描述了支撑在一个边缘的初始状态并接近高斯连贯状态的初始状态的量子演变的半经典限制。我们通过图表上的liouville运算符来定义限制经典动力学，并通过kre \uın的自我伴侣操作员的奇异扰动理论获得。对于同一类的初始状态，我们研究了这对$ $（h_k，h_ {d}^{\ oplus}）$的波和散射操作员的半经典限制，其中$ h_ {d}^{\ oplus} $是带有dirichlet条件的dirichlet条件。
We consider the dynamics of a quantum particle of mass $m$ on a $n$-edges star-graph with Hamiltonian $H_K=-(2m)^{-1}\hbar^2 Δ$ 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 Kre\uın'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 $(H_K,H_{D}^{\oplus})$, where $H_{D}^{\oplus}$ is the free Hamiltonian with Dirichlet conditions in the vertex.
