Exact WKB analysis produces median-summed spectra and an algebraic equation for the exceptional point of PT-symmetry breaking in the inverted triple-well system.
Instantons in Quantum Mechanics and Resurgent Expansions
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abstract
Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical case, the eigenvalue may be expressed in terms of a generalized perturbative expansion (resurgent expansion). Modified Bohr-Sommerfeld quantization conditions lead to generalized perturbative expansions which may be expressed in terms of nonanalytic factors of the form exp(-a/g), where a > 0 is the instanton action, and power series in the coupling g, as well as logarithmic factors. The ground-state energy, for the specific Hamiltonians, is shown to be dominated by instanton effects, and we provide numerical evidence for the validity of the related conjectures.
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Presents explicit trans-series calculations for the double-well spectrum via exact WKB and path integral approaches up to four-instanton level.
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Exact WKB analysis of inverted triple-well: resonance, PT-symmetry breaking, and resurgence
Exact WKB analysis produces median-summed spectra and an algebraic equation for the exceptional point of PT-symmetry breaking in the inverted triple-well system.
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The Double Well Done Doubly-Well
Presents explicit trans-series calculations for the double-well spectrum via exact WKB and path integral approaches up to four-instanton level.