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Phase rigidity and avoided level crossings in the complex energy plane
Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany, Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation.
Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany.
Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
2006 (English)In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 74, no 5Article in journal (Refereed) Published
Abstract [en]

We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions ?, and define the value r? = (?/?) ?/? that characterizes the phase rigidity of the eigenfunctions ?. In the scenario with avoided level crossings, r? varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of r? is an internal property of an open quantum system. In the literature, the phase rigidity ? of the scattering wave function ?CE is considered. Since ?CE can be represented in the interior of the system by the ?, the phase rigidity ? of the ?CE is related to the r? and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity ? 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 ? and transmission numerically for small open cavities. © 2006 The American Physical Society.

Place, publisher, year, edition, pages
2006. Vol. 74, no 5
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-50069DOI: 10.1103/PhysRevE.74.056204OAI: oai:DiVA.org:liu-50069DiVA: diva2:270965
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-11

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Sadreev, Almas

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The Institute of TechnologyDepartment of Physics, Chemistry and Biology
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