无序玻色子的相干势近似
Coherent potential approximation for disordered bosons
摘要：
介绍了玻色子准粒子激发的一类随机模型，如无序固体的振动。这些模型的线性化相空间动力学的生成器是确定性和随机部分的总和。前者可以描述任意N个全同声子带的模型，而后者是Lueck，Sommers，and Zirnbauer（LSZ）的随机矩阵模型的d维推广。模型的构建，以排除失控的解决方案的非物理发生。利用Efetov-Wegner超对称性方法和超玻色化新技术，将无序玻色模型转化为超矩阵场论的形式。将场论作为变分问题处理，得到了平均场型的自洽近似。由此产生的方案，被称为相干势近似，成为精确的大值N。在随机矩阵极限下，与LSZ的结果一致。数值求解了全d维问题的自洽方程。
英文摘要：
A family of random models for bosonic quasi-particle excitations, e.g. the vibrations of a disordered solid, is introduced. The generator of the linearized phase space dynamics of these models is the sum of a deterministic and a random part. The former may describe any model of N identical phonon bands, while the latter is a d-dimensional generalization of the random matrix model of Lueck, Sommers, and Zirnbauer (LSZ). The models are constructed so as to exclude the unphysical occurrence of runaway solutions. By using the Efetov-Wegner supersymmetry method in combination with the new technique of superbosonization, the disordered boson model is cast in the form of a supermatrix field theory. A self-consistent approximation of mean-field type arises from treating the field theory as a variational problem. The resulting scheme, referred to as a coherent potential approximation, becomes exact for large values of N. In the random-matrix limit, agreement with the results of LSZ is found. The self-consistency equation for the full d-dimensional problem is solved numerically.
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