Second-Order Perturbation in Adaptive Perturbation Method

The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all diagonal elements for a Fock state. We consider the harmonic oscillator with the interacting term, λ۱x۴/۶ + λ۲x۶/۱۲۰, where λ۱ and λ۲ are coupling constants, and x  is the position operator. The spectrum shows a quantitative result from the second-order, less than ۱ percent error, compared to a numerical solution when turning off the λ۲. When we turn on the λ۲, more deviation occurs, but the error is still less than ۲ percent. We show a quantitative result beyond a weak-coupling region. Our study should provide interest in the holographic principle and strongly coupled boundary theory.

کلیدواژه ها:

Fock State ، Harmonic Oscillator ، QFT ، Hamiltonian ، Strongly Coupled Physics