Weniger变换在求非谐振子无穷耦合极限中的应用  

Application of the Weniger’s Transformation in Approximations of Infinite Coupling Limits of Anharmonic Oscillators

作　　者：姚清照 贺黎明[1] YAO Qingzhao;HE Liming(Department of Physics,East China University of Science and Technology,Shanghai 200237,China)

机构地区：[1]华东理工大学物理系,上海200237

出　　处：《华东理工大学学报（自然科学版）》2021年第3期370-377,共8页Journal of East China University of Science and Technology

摘　　要：研究了Weniger变换求非谐振子基态能强耦合微扰展开发散级数和,并计算出无穷耦合极限;使用计算机代数系统Maple克服了舍入误差对数值计算的负面影响,代价是每个数据的表示和运算会消耗更多的内存;提出一种优化数组结构的方案,有效地缓解了内存压力,在现有的内存资源下得到高精度的计算结果。During decades,nonlinear sequence transformations method has been well developed in fields of mathematics and physics,and extensive simulation results have demonstrated its power of the acceleration of convergence and the summation of divergent series.The perturbation expansions for the infinite coupling limits of the quartic,sextic and octic anharmonic oscillators are strongly divergent,and renormalization techniques shall be used to slow down its rate of divergence.This paper presents the performance of Weniger’s transformation in summation of the renormalized perturbation series,and gives numerical results of infinite coupling limits.With the help of computer algebra system Maple,which has abilities of rational arithmetics,we can get rid of the bad effect of rounding errors.However,Maple consumes large amounts of memory resources to store data and calculate,as a result memory overflow occurs frequently.Aiming at the above problem,this paper proposes a method to compress the dimensions of arrays in order to reduce load of storage,and thus we can obtain more accurate approximations of infinite coupling limits than the known method.

关 键 词：Weniger变换 非谐振子 计算机代数系统 

分 类 号：O241[理学—计算数学] O411[理学—数学]