Second-Order Perturbation in Adaptive Perturbation Method

Document Type : Regular article


Asia Center for Theoretical Physics


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, λ1x4/6 + λ2x6/120, where λ1 and λ2 are coupling constants, and x  is the position operator. The spectrum shows a quantitative result from the second-order, less than 1 percent error, compared to a numerical solution when turning off the λ2. When we turn on the λ2, more deviation occurs, but the error is still less than 2 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.


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Volume 2, Issue 4
November 2022
Pages 37-44
  • Receive Date: 12 August 2022
  • Revise Date: 26 September 2022
  • Accept Date: 28 September 2022