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Diabolic Points, Geometric Phases, and Quantum Chaos

  • Dirk Dubbers
  • Hans-Jürgen Stöckmann
Part of the Graduate Texts in Physics book series (GTP)

Abstract

Quantum systems have a number of peculiar features that can all be traced back to one common origin, namely the universal “diabolic” shapes of energy surfaces in the vicinity of a degeneracy. The first such feature is the avoided-crossing effect, when energy levels do not cross but seem to repel each other when plotted in dependence of an external parameter. The next feature is the occurrence of geometric phases, also known as Berry phases, which accumulate during excursions in parameter space. We discuss experimental examples of such phases, both in the space of magnetic fields and in what we call the space of shapes. The Aharonov–Bohm phase is closely related to such geometric phases. Finally, in a short section we show that the hallmarks of quantum chaos can be understood in terms of locally defined 2×2 matrices and their avoided level crossings.

Keywords

Chaotic System Current Sheet Pure Spin Quadrupole Interaction Geometric Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dirk Dubbers
    • 1
  • Hans-Jürgen Stöckmann
    • 2
  1. 1.Fak. Physik und Astronomie, Physikalisches InstitutUniversität HeidelbergHeidelbergGermany
  2. 2.Fachbereich Physik Philipps-Universität MarburgMarburgGermany

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