The quantum instanton rate reduces to semiclassical instanton theory only for symmetric barriers; for asymmetric barriers a spurious low-energy path ruins the approximation, and a projection operator fixes it.
Jang \ and\ author G
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Semiclassical analysis of the quantum instanton approximation
The quantum instanton rate reduces to semiclassical instanton theory only for symmetric barriers; for asymmetric barriers a spurious low-energy path ruins the approximation, and a projection operator fixes it.