Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations

In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Thosesystems have physical applications in soil science, mathematical biology, and invariant curve flows in R^3. Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.     

可积系统规则运动的量子经典对应与有关问题

基于表述经典及量子系统可积性的动力对称性群,对量子可积系统规则运动的经典对应问题运用归纳法进行了研究.具体给出了经典近似描述的适用条件,并进行了简明讨论.Based on the dynamical symmetry group characterizing the integrability of classical as well as quantum mechanics, quantum dynamics with proper initial conditions was genuinely formulated, and analytical solutions in the form of soliton-like state evolving around a certain invariant torus were obtained. It has been shown that, in case the intrinsic size of the evolving quantum state is significantly smaller than the extent of its evolving orbit, the motion can be satisfactorily treated with...     

氢原子能级简并度与对称性的关系

1 能级简并与对称性关系的一般讨论 用量子力学处理实际问题时,体系各能级的简并度(或权重)是极为重要的.如何判断一个体系的能级是否简并,量子力学中有一条定理[1]:     

轻核中的U(90)动力学对称性

在IBM4中,当存在s、d、g玻色子时,体系的对称性群为U(90).本文研究了子群链:U₉₀ U₁₅(sdg)×U₆(ST) SU₁₅(sdg)×U₆(ST) SU₅(sdg)× O₆(ST) SO₅(dg)×O₃(S)×O₃(T) O₃(dg)×O₃(S)×O₃(T) O₃(J)×O₃(T)给出了约化规则和典型能谱,并在轻核中找到了具有这种动力学对称性的能谱的例子,偶偶核³⁴S与奇奇核 ³⁴Cl在一个多重态中.