Abstract
It is shown that with asymmetric classical vacua the quantum mechanical instanton approach to the energy splitting of degenerate states applies even though the degenerate state in one well is not the quantum mechanical ground state of that well. The instanton approach leads to the correct leading exponential behavior of the energy splitting ΔE, but the prefactor is much more difficult to compute due to the asymmetric nature of the fluctuation potential V″(φc(t)), which is in turn a direct consequence of the asymmetry of the two classical minima between which the instanton interpolates.
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Note that if k is odd, then 〈φL|L,k〉=0, so we should instead compute a transition amplitude from the first central peak of the wavefunction in the left-hand well rather than from the very center of the left-hand well.
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Dunne, G.V. Instantons and Asymmetric Vacua. Foundations of Physics 30, 463–474 (2000). https://doi.org/10.1023/A:1003625924025
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DOI: https://doi.org/10.1023/A:1003625924025