论文标题
自适应扰动方法中的二阶扰动
Second-Order Perturbation in Adaptive Perturbation Method
论文作者
论文摘要
扰动方法是具有可解决领先顺序的近似方案。标准方法是为领先顺序选择一个非相互作用的部门。自适应扰动方法通过将所有对角线元素用于FOCK状态来改善可解的部分。我们考虑具有相互作用术语的谐波振荡器，$λ_1x^4/6+λ_2X^6/120 $，其中$λ_1$和$λ_2$是耦合常数，而$ x $是位置操作员。与关闭$λ_2$的数值解决方案相比，频谱显示了二阶的定量结果，小于1％的误差。当我们打开$λ_2$时，会发生更多偏差，但错误仍然不到2％。我们显示出超出弱耦合区域的定量结果。我们的研究应对全息原理和强烈耦合边界理论产生兴趣。
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, $λ_1x^4/6+λ_2x^6/120$, where $λ_1$ and $λ_2$ 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 $λ_2$. When we turn on the $λ_2$, 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.
