Phys. Rev. A 80, 042104 (2009) [9 pages]Decaying and growing eigenmodes in open quantum systems: Biorthogonality and the Petermann factorReceived 24 March 2009; published 6 October 2009 We study the biorthogonality between decaying and growing eigenmodes in one-dimensional potential barrier problems. It is shown that Petermann factors Kn of the eigenmodes, a measure of nonorthogonality, are involved in decaying mechanism of an initially confined particle. We also show that the decay tail of the growing modes at an exceptional point (EP), where Kn become infinite, is not exponential, but ∼t2e−ΓEPt, ΓEP the decay rate of the decaying mode at EP. In addition, the geometrical phase near an EP is illustrated by the evolution of wave function. © 2009 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.80.042104
DOI:
10.1103/PhysRevA.80.042104
PACS:
03.65.Ge, 02.30.Mv, 24.30.Gd, 42.50.Lc
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