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Accidental degeneracy and berry phase of resonant states

  • Causality, Semigroups And Resonance States
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Irreversibility and Causality Semigroups and Rigged Hilbert Spaces

Part of the book series: Lecture Notes in Physics ((LNP,volume 504-504))

Abstract

We study the complex geometric phase acquired by the resonant states of an open quantum system which evolves irreversibly in a slowly time dependent environment. In analogy with the case of bound states, the Berry phase factors of resonant states are holonomy group elements of a complex line bundle with structure group C*. In sharp contrast with bound states, accidental degeneracies of resonances produce a continuous closed line of singularities formally equivalent to a continuous distribution of “magnetic” charge on a “diabolical” circle, in consequence, we find different classes of topologically inequivalent non-trivial closed paths in parameter space.

This work was partially supported by CONACYT (México) under contract No. 4964-E9406

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Authors and Affiliations

  1. Instituto de Física, UNAM, Apartado Postal 20-364, 01000, México D.F., Mexico

    A. Mondragón & E. Hernández

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  1. A. Mondragón
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  2. E. Hernández
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Arno Bohm Heinz-Dietrich Doebner Piotr Kielanowski

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© 1998 Springer-Verlag

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Mondragón, A., Hernández, E. (1998). Accidental degeneracy and berry phase of resonant states. In: Bohm, A., Doebner, HD., Kielanowski, P. (eds) Irreversibility and Causality Semigroups and Rigged Hilbert Spaces. Lecture Notes in Physics, vol 504-504. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106786

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  • DOI: https://doi.org/10.1007/BFb0106786

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64305-0

  • Online ISBN: 978-3-540-69725-1

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