CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia, European Union.
Phys Rev E. 2018 Jan;97(1-1):012206. doi: 10.1103/PhysRevE.97.012206.
We perform a detailed numerical study of diffusion in the ɛ stadium of Bunimovich, and propose an empirical model of the local and global diffusion for various values of ɛ with the following conclusions: (i) the diffusion is normal for all values of ɛ (≤0.3) and all initial conditions, (ii) the diffusion constant is a parabolic function of the momentum (i.e., we have inhomogeneous diffusion), (iii) the model describes the diffusion very well including the boundary effects, (iv) the approach to the asymptotic equilibrium steady state is exponential, (v) the so-called random model (Robnik et al., 1997) is confirmed to apply very well, (vi) the diffusion constant extracted from the distribution function in momentum space and the one derived from the second moment agree very well. The classical transport time, an important parameter in quantum chaos, is thus determined.
我们对 Bunimovich 的 ε 体育场中的扩散进行了详细的数值研究，并提出了一个局部和全局扩散的经验模型，用于各种 ε 值，得出以下结论：（i）对于所有 ε 值（≤0.3）和所有初始条件，扩散都是正常的；（ii）扩散常数是动量的抛物线函数（即，我们具有非均匀扩散）；（iii）该模型很好地描述了扩散，包括边界效应；（iv）达到渐近平衡稳态的方式是指数的；（v）所谓的随机模型（Robnik 等人，1997 年）被证实非常适用；（vi）从动量空间中的分布函数中提取的扩散常数和从二阶矩中导出的扩散常数非常吻合。因此，经典的输运时间，量子混沌中的一个重要参数，被确定了。
