Barocchi Fabrizio, Bafile Ubaldo, Sampoli Marco
Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 1):022102. doi: 10.1103/PhysRevE.85.022102. Epub 2012 Feb 17.
We show that an exact solution of the generalized Langevin equation (GLE) for the autocorrelations of a many-body classical system can be given in an exponential functionality (EF) form. As a consequence, the power spectrum of the correlation has a Lorentzian functionality, i.e., is represented by an infinite sum of Lorentzian functions corresponding to the eigenmodes of the considered correlation. By means of the simple derivation of the GLE by M. H. Lee [Phys. Rev. B 26, 2547 (1982)], we also show that, in practical cases of interest to experimental spectroscopies, possible approximations of the EF are related to a reduction of the relevant dynamical variables via a restriction of the dimensions of the orthogonalized space onto which the dynamics of the system is projected.
我们表明，对于多体经典系统自相关的广义朗之万方程（GLE）的精确解可以用指数函数形式给出。因此，相关的功率谱具有洛伦兹函数形式，即由对应于所考虑相关性本征模的洛伦兹函数的无穷和表示。借助于M. H. 李 [《物理评论B》26, 2547 (1982)] 对GLE的简单推导，我们还表明，在实验光谱学感兴趣的实际情况下，指数函数形式的可能近似与通过限制系统动力学所投影到的正交空间的维度来减少相关动力学变量有关。
