Quantum Imprint of the Anharmonic Oscillator
- URL: http://arxiv.org/abs/2308.01244v1
- Date: Wed, 2 Aug 2023 15:58:33 GMT
- Title: Quantum Imprint of the Anharmonic Oscillator
- Authors: Prisco Lo Chiatto, Sebastian Schenk, Felix Yu
- Abstract summary: We study the anharmonic double well in quantum mechanics using exact Wentzel-Kramers-Brillo (WKB) methods.
We compute the tunneling action in this double scaling limit, and compare it to the transition amplitude from the vacuum to a highly excited state.
Our results, exact in the semiclassical limit, show that the two expressions coincide, apart from an irreducible and surprising instanton contribution.
- Score: 1.675857332621569
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the anharmonic double well in quantum mechanics using exact
Wentzel-Kramers-Brillouin (WKB) methods in a 't Hooft-like double scaling limit
where classical behavior is expected to dominate. We compute the tunneling
action in this double scaling limit, and compare it to the transition amplitude
from the vacuum to a highly excited state. Our results, exact in the
semiclassical limit, show that the two expressions coincide, apart from an
irreducible and surprising instanton contribution. Thus, the semiclassical
limit of the anharmonic oscillator betrays its quantum origin as a rule, which
we dub the "quantum imprint rule," showing that the quantum theory is
intrinsically gapped from classical behavior. Besides an example of the failure
of reductionism and an example of a resurgent connection between perturbative
and nonperturbative physics, this work provides a possible classification of
theories according to their quantum imprints.
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