Impact of initial fluctuations on the dissipative dynamics of interacting Fermi systems: A model case study
Impact of initial fluctuations on the dissipative dynamics of interacting Fermi systems: A model case study
复制标题
初始涨落对相互作用的费米系统耗散动力学的影响：模型案例研究
作者：
Ibrahim Ulgen;B. Yilmaz;D. Lacroix
用于计算量子多体系统动力学的标准方法是平均场(MF)近似，例如依赖时间的Hartree-Fock(TDHF)方法。尽管MF方法相当成功，但它们也存在一些众所周知的缺点，其中之一是集体行动的消散不足。随机平均场方法(SMF)考虑了一组具有随机初始条件的MF轨迹，是考虑平均场以外的耗散效应的一个很好的候选方法。在该方法中，首先将单体密度矩阵元处理为一组随机的高斯c数，然后对其进行调整以再现集体单体可观测量的一阶矩和二阶矩。结果表明，通过放宽对初始概率的高斯假设，可以进一步提高SMF方法的预测能力。更准确地说，对矩阵元素使用高斯分布或均匀分布通常会导致长时间的过阻尼，而峰度较小的分布会更好地再现长时间演化。
Standard methods used for computing the dynamics of a quantum many-body system are the mean-field (MF) approximations such as the time-dependent Hartree-Fock (TDHF) approach. Even though MF approaches are quite successful, they suffer some well-known shortcomings, one of which is insufficient dissipation of collective motion. The stochastic mean-field approach (SMF), where a set of MF trajectories with random initial conditions are considered, is a good candidate to include dissipative effects beyond mean field. In this approach, the one-body density matrix elements are treated initially as a set of stochastic Gaussian c numbers that are adjusted to reproduce first and second moments of collective one-body observables. It is shown that the predictive power of the SMF approach can be further improved by relaxing the Gaussian assumption for the initial probabilities. More precisely, using Gaussian or uniform distributions for the matrix elements generally leads to overdamping for long times, whereas distributions with smaller kurtosis lead to much better reproduction of the long time evolution.