dorsal/arxiv
View SchemaPower-Law Energy Splitting Generated By Tunneling Between Non-smooth Tori
| Authors | Z. Q. Bai |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0110126 |
| URL | https://arxiv.org/abs/quant-ph/0110126 |
| DOI | 10.1088/0305-4470/35/8/307 |
| Journal | J.Phys.A: Math. Gen. 35(2002)1895 (fwd) |
Abstract
We discuss the energy level splitting $\Delta\epsilon$ due to quantum tunneling between congruent tori in phase space. In analytic cases, it is well known that $\Delta\epsilon$ 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 $\Delta\epsilon$ is derived, which shows that $\Delta \epsilon$ decays as $\hbar^{k+1}$ when $\hbar\to 0$ with k being the order of non-smoothness.
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"abstract": "We discuss the energy level splitting $\\Delta\\epsilon$ due to quantum\ntunneling between congruent tori in phase space. In analytic cases, it is well\nknown that $\\Delta\\epsilon$ decays faster than power of $\\hbar$ in the\nsemi-classical limit. This is not true in non-smooth cases, specifically, when\nthe tori are connected by line on which the Hamiltonian is not smooth. Under\nthe assumption that the non-smoothness depends only upon the x- or\np-coordinate, the leading term in the semi-classical expansion of\n$\\Delta\\epsilon$ is derived, which shows that $\\Delta \\epsilon$ decays as\n$\\hbar^{k+1}$ when $\\hbar\\to 0$ with k being the order of non-smoothness.",
"arxiv_id": "quant-ph/0110126",
"authors": [
"Z. Q. Bai"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/35/8/307",
"journal_ref": "J.Phys.A: Math. Gen. 35(2002)1895 (fwd)",
"title": "Power-Law Energy Splitting Generated By Tunneling Between Non-smooth Tori",
"url": "https://arxiv.org/abs/quant-ph/0110126"
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