Structural aspects of FRG in quantum tunnelling 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(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.

19 pages, 7 figures

References in corpus (7)

• Exact evolution equation for the effective potential
• The Standard Model Higgs boson as the inflaton
• Flow Equation for Supersymmetric Quantum Mechanics
• Convergence of Derivative Expansion in Supersymmetric Functional RG Flows
• Impact of New Physics on the EW vacuum stability in a curved spacetime background
• Direct Higgs-gravity interaction and stability of our Universe
• Optimized regulator for the quantized anharmonic oscillator

Cited by in corpus (5)

• Regular Black Holes from Proper-Time flow in Quantum Gravity and their Quasinormal modes, Shadow and Hawking radiation
• Tunneling with physics-informed RG flows in the anharmonic oscillator
• RG studies of scalar-field models of long-range interactions
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
• The $\theta$-vacuum from functional renormalisation