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Power-Law Energy Splitting Generated By Tunneling Between Non-smooth Tori | | Z. Q. Bai
; | | Date: |
21 Oct 2001 | | Journal: | J.Phys.A: Math. Gen. 35(2002)1895 (fwd) | | Subject: | quant-ph | | Abstract: | We discuss the energy level splitting $Deltaepsilon$ due to quantum tunneling between congruent tori in phase space. In analytic cases, it is well known that $Deltaepsilon$ 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 $Deltaepsilon$ is derived, which shows that $Delta epsilon$ decays as $hbar^{k+1}$ when $hbar o 0$ with k being the order of non-smoothness. | | Source: | arXiv, quant-ph/0110126 | | Services: | Forum | Review | PDF | Favorites | |
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