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Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems
Abstract : 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.
Cited literature [31 references]
https://hal.archives-ouvertes.fr/hal-01633049
Contributor : Amaury Mouchet Connect in order to contact the contributor
Submitted on : Saturday, January 13, 2018 - 4:06:24 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:10 PM
Long-term archiving on: : Saturday, May 5, 2018 - 6:28:55 PM
Contributor : Amaury Mouchet Connect in order to contact the contributor
Submitted on : Saturday, January 13, 2018 - 4:06:24 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:10 PM
Long-term archiving on: : Saturday, May 5, 2018 - 6:28:55 PM
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