arXiv quant-ph/06050562006-05quant-ph

相位刚性和避免复杂能量平面中的水平交叉

Phase rigidity and avoided level crossings in the complex energy plane

E. N. Bulgakov, I. Rotter, A. F. Sadreev

备注：: 6 pages, 3 figures
DOI：: 10.1103/PhysRevE.74.056204

摘要：

我们考虑一个开放量子系统的有效哈密顿量，它的双正交本征函数$ϕ_λ$和定义值$r_λ= (ϕ_λ|ϕ_λ)/<ϕ_λ|ϕ_λ>$，表征相位刚性的本征函数$ϕ_λ$。在具有避免的电平交叉的场景中，由于相邻谐振的相互影响，$r_λ$在1和0之间变化。$r_λ$的变化可以被认为是{ \it开放}量子系统的内部性质。在文献中，相位刚性$ρ$的散射波函数$Ψ^E_C$被认为是。由于$Ψ^E_C$在系统内部可以由$ϕ_λ$表示，因此$Ψ^E_C$的相位刚性$ρ$与$r_λ$相关，因此也与相邻共振的相互影响相关。因此，相位刚性$ρ$减小到小于1的值应至少部分地被认为是重叠区域中的开放量子系统的内部性质。与诸如通过量子点的透射率的可测量值的关系，从透射率在任何情况下相对于有效哈密顿量共振的事实得出。我们用数值方法说明了相位刚度$ρ$和小开口腔的透射率之间的关系。

英文摘要：

We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions $ϕ_λ$ and define the value $r_λ= (ϕ_λ|ϕ_λ)/<ϕ_λ|ϕ_λ>$ that characterizes the phase rigidity of the eigenfunctions $ϕ_λ$. In the scenario with avoided level crossings, $r_λ$ varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of $r_λ$ may be considered as an internal property of an {\it open} quantum system. In the literature, the phase rigidity $ρ$ of the scattering wave function $Ψ^E_C$ is considered. Since $Ψ^E_C$ can be represented in the interior of the system by the $ϕ_λ$, the phase rigidity $ρ$ of the $Ψ^E_C$ is related to the $r_λ$ and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity $ρ$ to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant with respect to the effective Hamiltonian. We illustrate the relation between phase rigidity $ρ$ and transmission numerically for small open cavities.

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