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Power-Law Energy Splitting Generated By Tunneling Between Non-smooth Tori

Z. Q. Bai
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Abstract

We discuss the energy level splitting $Δε$ due to quantum tunneling between congruent tori in phase space. In analytic cases, it is well known that $Δε$ decays faster than power of $\hbar$ in the semi-classical limit. This is not true in non-smooth cases, specifically, when the tori are connected by line on which the Hamiltonian is not smooth. Under the assumption that the non-smoothness depends only upon the x- or p-coordinate, the leading term in the semi-classical expansion of $Δε$ is derived, which shows that $Δε$ decays as $\hbar^{k+1}$ when $\hbar\to 0$ with k being the order of non-smoothness.

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Z. Q. Bai. 2001-12-20. Power-Law Energy Splitting Generated By Tunneling Between Non-smooth Tori. https://doi.org/10.1088/0305-4470%2F35%2F8%2F307

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