Structural aspects of FRG in quantum tunnelling computations
- URL: http://arxiv.org/abs/2206.06917v1
- Date: Tue, 14 Jun 2022 15:23:25 GMT
- Title: Structural aspects of FRG in quantum tunnelling computations
- Authors: Alfio Bonanno, Alessandro Codello, Dario Zappala'
- Abstract summary: We probe both the unidimensional quartic harmonic oscillator and the double well potential.
Two partial differential equations for the potential V_k(varphi) and the wave function renormalization Z_k(varphi) are studied.
- Score: 68.8204255655161
- License: http://creativecommons.org/publicdomain/zero/1.0/
- Abstract: We probe both the unidimensional quartic harmonic oscillator and the double
well potential through a numerical analysis of the Functional Renormalization
Group flow equations truncated at first order in the derivative expansion. The
two partial differential equations for the potential V_k(varphi) and the wave
function renormalization Z_k(varphi), as obtained in different schemes and with
distinct regulators, are studied down to k=0, and the energy gap between lowest
and first excited state is computed, in order to test the reliability of the
approach in a strongly non-perturbative regime. Our findings point out at least
three ranges of the quartic coupling lambda, one with higher lambda where the
lowest order approximation is already accurate, the intermediate one where the
inclusion of the first correction produces a good agreement with the exact
results and, finally, the one with smallest lambda where presumably the higher
order correction of the flow is needed. Some details of the specifics of the
infrared regulator are also discussed.
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