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Phase rigidity and avoided level crossings in the complex energy plane
Evgeny N Bulgakov1, Ingrid Rotter, Almas F Sadreev
1Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany. ben@tnp.krasn.ru
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
Summary
We introduce a new measure, r(lambda), to quantify phase rigidity in open quantum systems. This internal property, related to resonance interactions, influences measurable quantities like quantum dot transmission.
Area of Science:
- Quantum Mechanics
- Condensed Matter Physics
Background:
- Open quantum systems exhibit complex behaviors due to interactions with their environment.
- Phase rigidity is a crucial property characterizing the stability and behavior of quantum wave functions.
Purpose of the Study:
- To define and investigate a new metric, r(lambda), for phase rigidity of biorthogonal eigenfunctions in open quantum systems.
- To explore the relationship between this internal phase rigidity and the influence of neighboring resonances.
- To connect the concept of phase rigidity to measurable quantities like transmission through quantum systems.
Main Methods:
- Consideration of the effective Hamiltonian for open quantum systems.
- Definition of the phase rigidity value r(lambda) for biorthogonal eigenfunctions.
- Analysis of r(lambda) in scenarios with avoided level crossings.
- Numerical illustration of the relationship between phase rigidity (rho) and transmission in small open cavities.
Main Results:
- The value r(lambda) quantifies the phase rigidity of eigenfunctions and varies between 1 and 0 due to resonance interactions.
- The variation of r(lambda) is an intrinsic property of the open quantum system.
- Phase rigidity (rho) of scattering wave functions is linked to r(lambda) and resonance interactions.
- Reduced phase rigidity in the overlapping regime is partly an internal system property.
Conclusions:
- Phase rigidity, characterized by r(lambda), is an internal property of open quantum systems influenced by resonance interactions.
- This internal property directly relates to the phase rigidity of scattering wave functions.
- The findings provide a theoretical basis for understanding measurable phenomena like transmission through quantum dots.
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