Savin Dmitry V, Sommers Hans-Jürgen
Fachbereich Physik, Universität Duisburg-Essen, 45117 Essen, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 2):035201. doi: 10.1103/PhysRevE.69.035201. Epub 2004 Mar 11.
The reflection matrix R=S(dagger)S, with S being the scattering matrix, differs from the unit matrix when absorption is finite. Using the random matrix approach, we calculate analytically the distribution function of its eigenvalues in the limit of a large number of propagating modes in the leads attached to a chaotic cavity. The obtained result is independent of the presence of time-reversal symmetry in the system, being valid at finite absorption and arbitrary openness of the system. The particular cases of perfectly and weakly open cavities are considered in detail. An application of our results to the problem of thermal emission from random media is briefly discussed.
反射矩阵(R = S^{\dagger}S)（其中(S)为散射矩阵），当存在有限吸收时，它与单位矩阵不同。利用随机矩阵方法，我们在连接到混沌腔的引线中有大量传播模式的极限情况下，解析地计算了其特征值的分布函数。所得结果与系统中时间反演对称性的存在无关，在有限吸收和系统任意开放度的情况下均有效。详细考虑了完全开放和弱开放腔的特殊情况。简要讨论了我们的结果在随机介质热发射问题中的应用。
