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.
Ma, C. (2022). Second-Order Perturbation in Adaptive Perturbation Method. Journal of Holography Applications in Physics, 2(4), 37-44. doi: 10.22128/jhap.2022.586.1034
MLA
Chen-Te Ma. "Second-Order Perturbation in Adaptive Perturbation Method". Journal of Holography Applications in Physics, 2, 4, 2022, 37-44. doi: 10.22128/jhap.2022.586.1034
HARVARD
Ma, C. (2022). 'Second-Order Perturbation in Adaptive Perturbation Method', Journal of Holography Applications in Physics, 2(4), pp. 37-44. doi: 10.22128/jhap.2022.586.1034
VANCOUVER
Ma, C. Second-Order Perturbation in Adaptive Perturbation Method. Journal of Holography Applications in Physics, 2022; 2(4): 37-44. doi: 10.22128/jhap.2022.586.1034
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