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低维无序系统本征问题的快速求解方法
发表时间：2012-02-15 浏览量：1556 下载量：764
| 全部作者： | 徐慧，郭锐，朱佳，马松山 |
| 作者单位： | 中南大学物理科学与技术学院 |
| 摘 要： | 在Dean本征值方法的基础上，建立均分法的本征值算法模型；将均分法的计算结果与反幂法及追赶法等数值方法相结合，得到一个低维无序系统的本征值和本征矢的快速算法；将此方法应用于计算低维无序体系的局域长度，得到不同无序度对体系局域长度的影响。结果表明：在大尺度系统中，与其他无序本征算法对比，均分法计算本征值不仅速度优于步进法的本征值算法，且对本征值精度运算可实时控制，而所研究的本征矢方法性能与其他方法相比亦有很大提升，将此2种方法综合使用能进一步提高解决无序系统本征问题的效率，并且在处理大型系统时，优势更加明显；通过该方法对低维无序系统的计算，表明随着无序度的增大，局域长度迅速缩短，系统导电性能降低，系统总能减少。 |
| 关 键 词： | 低维物理；均分法；Dean算法；无序系统；本征值 |
| Title： | A rapid method of solving eigen problem of low-dimension disordered system |
| Author： | XU Hui, GUO Rui, ZHU Jia, MA Songshan |
| Organization： | College of Physics Science and Technology, Central South University |
| Abstract： | Based on the Dean eigenvalue method, the split method of eigenvalue was established. Combining the result of split method with inverse power method and pursuit method, a fast algorithm of eigenvalue and eigenvector for lower-dimensional disordered systems was obtained. This algorithm was used in calculating the local length of low-dimensional disordered system and to obtain the influence of different disorder degree on the local length. By comparing with other methods, the result indicates that calculating the eigenvalue with the split method is not only faster than step-by-step method but also good at controlling the precision calculation of the eigenvalue; the eigenvector calculating method also holds a better property, and this advantage increases as the system expands. Integrating of both methods can further increase the speed of solving eigen problem of disordered system, and the advantage is more obvious in handling the problems in large systems. At last, by applying the methods to low-dimensional disordered system, it is found that the local length shortens sharply, the conductance decreases, and total energy reduces along with the increasing of disorder degree. |
| Key words： | low dimensional physics; split method; Dean algorithm; disordered system; eigenvalue |
| 发表期数： | 2012年2月第3期 |
| 引用格式： | 徐慧，郭锐，朱佳，等. 低维无序系统本征问题的快速求解方法[J]. 中国科技论文在线精品论文，2012，5（3）：219-226. |
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