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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2017

Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems

Hiromitsu Harada
  • Fonction : Auteur
Akira Shudo
  • Fonction : Auteur

Résumé

The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann surface provides complete information on the topology of complex paths, which allows us to enumerate all the possible candidates contributing to the semiclassical sum formula for tunnelling splittings. This naturally leads to action relations among classically disjoined regions, revealing entirely non-local nature in the quantization condition. The importance of the proper treatment of Stokes phenomena is also discussed in Hamiltonians in the normal form.
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Dates et versions

hal-01633049 , version 1 (13-01-2018)

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Hiromitsu Harada, Amaury Mouchet, Akira Shudo. Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems. Journal of Physics A: Mathematical and Theoretical, 2017, 50 (43), ⟨10.1088/1751-8121/aa8c67⟩. ⟨hal-01633049⟩
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