Phase rigidity and avoided level crossings in the complex energy plane.
نویسندگان
چکیده
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))/ 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) is an internal property of an open quantum system. In the literature, the phase rigidity rho of the scattering wave function Psi(C)(E) is considered. Since Psi(C)(E) can be represented in the interior of the system by the phi(lambda), the phase rigidity rho of the Psi(C)(E) 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 at energies that are determined by the real part of the eigenvalues of the effective Hamiltonian. We illustrate the relation between phase rigidity rho and transmission numerically for small open cavities.
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ar X iv : q ua nt - p h / 06 05 05 6 v 2 9 A ug 2 00 6 Phase rigidity and avoided level crossings in the complex energy plane
We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions φλ and define the value rλ = (φλ|φλ)/〈φλ|φλ〉 that characterizes the phase rigidity of the eigenfunctions φλ. In the scenario with avoided level crossings, rλ varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of rλ may be considered as an internal property of...
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ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 74 5 Pt 2 شماره
صفحات -
تاریخ انتشار 2006