Avoided level crossings and singular points |
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Authors: | Ingrid Rotter |
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Institution: | (1) Max-Planck-Institut fur Physik komplexer Systeme, D-01187 Dresden, Germany |
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Abstract: | Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points (BPs)
which are singular points in the complex energy plane. They cannot be identified with exceptional points. At a BP width bifurcation
occurs, different Riemann sheets evolve and the levels do not cross anymore when the system is still further opened. The BPs
are physically meaningful: they influence the dynamics of open as well as of closed quantum systems. The geometric phase that
arises by encircling a BP, is different from the phase that appears by encircling a diabolic point. This is found to be true
even for the two BPs into which the diabolic point is unfolded by opening the system.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. |
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Keywords: | open quantum systems singular points branch points exceptional points |
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