Tunneling in cosine potential with periodic boundary conditions

Abstract

In this paper we discuss three methods to calculate energy splitting in cosine potential on a circle, Bloch waves, semi--classical approximation and restricted basis approach. While the Bloch wave method gives only a qualitative result, with the WKB method we are able to determine its unknown coefficients. The numerical approach is most exact and enables us to extract further corrections to previous results.

9 pages, 3 figures

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• Theta dependence, sign problems and topological interference
• Resummation of not summable series

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