Structural aspects of FRG in quantum tunneling computations
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}(φ) and the wave function renormalization Z_{k}(φ) , 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 nonperturbative regime. Our findings point out at least three ranges of the quartic coupling λ, one with higher λ 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 λ where presumably the higher order correction of the flow is needed. Some details of the specifics of the infrared regulator are also discussed.
 Publication:

Annals of Physics
 Pub Date:
 October 2022
 DOI:
 10.1016/j.aop.2022.169090
 arXiv:
 arXiv:2206.06917
 Bibcode:
 2022AnPhy.44569090B
 Keywords:

 Functional renormalization;
 Quantum mechanics;
 Instanton;
 Tunneling;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 19 pages, 7 figures