Phase rigidity and avoided level crossings in the complex energy plane

Details Phase rigidity and avoided level crossings in the complex energy plane Phase rigidity and avoided level crossings in the complex energy plane

2006-05-05

arxiv.org/abs/quant-ph/0605056v2

Physics

Quantum Physics

6 pages, 3 figures

Scientific paper

10.1103/PhysRevE.74.056204

We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions $\phi_\lambda$ and define the value $r_\lambda = (\phi_\lambda|\phi_\lambda)/<\phi_\lambda|\phi_\lambda>$ that characterizes the phase rigidity of the eigenfunctions $\phi_\lambda$. In the scenario with avoided level crossings, $r_\lambda$ varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of $r_\lambda$ may be considered as an internal property of an {\it open} quantum system. In the literature, the phase rigidity $\rho$ of the scattering wave function $\Psi^E_C$ is considered. Since $\Psi^E_C$ can be represented in the interior of the system by the $\phi_\lambda$, the phase rigidity $\rho$ of the $\Psi^E_C$ is related to the $r_\lambda$ and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity $\rho$ 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 $\rho$ and transmission numerically for small open cavities.

Affiliated with

Also associated with

No associations

Rating

Phase rigidity and avoided level crossings in the complex energy plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Phase rigidity and avoided level crossings in the complex energy plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Phase rigidity and avoided level crossings in the complex energy plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-608040