Nonlinear response for external field and perturbation in the Vlasov system
Nonlinear response for external field and perturbation in the Vlasov system
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Vlasov 系统中外场和扰动的非线性响应
DOI：
10.1103/physreve.89.052114
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发表时间：
2014
影响因子：
2.4
通讯作者：
Shun Ogawa and Yoshiyuki Y. Yamaguchi
中科院分区：
文献类型：
--
作者：
伊藤 民武;伊賀 光博;山本 裕子;田丸博晴;吉田健一;Biju Vasudevan Pillai;石川 満;尾崎幸洋;H. Minamide and H. Ito;永田玲矢，横田光広;宮島信也;Fumiya Suenobu，Masaaki Ito，Fujio Kubo;Shun Ogawa and Yoshiyuki Y. Yamaguchi
利用瞬态线性化方法，给出了一维Vlasov系统的非线性响应理论。该理论包含了对外场和初始定态扰动的响应，甚至适用于二阶相变的临界点。我们应用该理论的哈密顿平均场模型，玩具模型的铁磁体，并调查的临界指数与外部磁场的响应在临界点特别。得到的临界指数为非经典值，而经典值为3。然而，有趣的是，在孤立的弗拉索夫系统中，一个标度关系与另一个非经典临界磁化率指数成立。通过直接模拟Vlasov方程的时间演化，数值证实了理论的有效性。
A nonlinear response theory is provided by use of the transient linearization method in the spatially one-dimensional Vlasov systems. The theory inclusively gives responses to external fields and to perturbations for initial stationary states, and is applicable even to the critical point of a second-order phase transition. We apply the theory to the Hamiltonian mean-field model, a toy model of a ferromagnetic body, and investigate the critical exponent associated with the response to the external field at the critical point in particular. The obtained critical exponent is the nonclassical value, while the classical value is 3. However, interestingly, one scaling relation holds with another nonclassical critical exponent of susceptibility in the isolated Vlasov systems. Validity of the theory is numerically confirmed by directly simulating temporal evolutions of the Vlasov equation.