This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are es...This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.展开更多
利用实空间重正化群(real space renormaligation group,RSRG)方法讨论自旋玻璃的3种不动点及临界指数,所得结果与严格解存在一定差距.大量研究表明,若选取较大的Kadanoff集团,则结果会好一些,但随着集团格点数的增大,计算量也大为增加...利用实空间重正化群(real space renormaligation group,RSRG)方法讨论自旋玻璃的3种不动点及临界指数,所得结果与严格解存在一定差距.大量研究表明,若选取较大的Kadanoff集团,则结果会好一些,但随着集团格点数的增大,计算量也大为增加,而研究没有提到其它更有效的修正方法.通过考虑能级和温度对重正化变换中集团概率的影响,在RSRG中引入权重因子重新推导重正化变换,得到新的不动点与临界指数,将其与修正前结果相对比,发现更接近严格解.展开更多
文摘This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.
文摘利用实空间重正化群(real space renormaligation group,RSRG)方法讨论自旋玻璃的3种不动点及临界指数,所得结果与严格解存在一定差距.大量研究表明,若选取较大的Kadanoff集团,则结果会好一些,但随着集团格点数的增大,计算量也大为增加,而研究没有提到其它更有效的修正方法.通过考虑能级和温度对重正化变换中集团概率的影响,在RSRG中引入权重因子重新推导重正化变换,得到新的不动点与临界指数,将其与修正前结果相对比,发现更接近严格解.
