Geometric phase for nonlinear oscillators from perturbative renormalization group
Geometric phase for nonlinear oscillators from perturbative renormalization group
复制标题
微扰重正化群非线性振子的几何相位
DOI：
10.1103/physreve.108.044215
复制
发表时间：
2023
影响因子：
2.4
通讯作者：
Pesin, D. A.
中科院分区：
文献类型：
--
作者：
Khromov, D. A.;Kryvoruchko, M. S.;Pesin, D. A.
我们制定了一个重整化群的方法来解决一般的非线性振子问题。该方法是基于相应的常微分方程的解所服从的精确群律。我们既考虑了具有时间无关参数的自治模型，也考虑了具有慢变参数的非自治模型。我们表明，重整化群方程的非自治的情况下，可以用来确定几何相位获得的振荡器在其参数的变化。我们通过将它们应用于货车der Pol和货车der Pol-Duffing模型来说明所得到的结果。
We formulate a renormalization-group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous models with time-independent parameters, as well as nonautonomous models with slowly varying parameters. We show that the renormalization-group equations for the nonautonomous case can be used to determine the geometric phase acquired by the oscillator during the change of its parameters. We illustrate the obtained results by applying them to the Van der Pol and Van der Pol-Duffing models.