Sound waves nearTcin a dynamic spherical model

The solution of the isotropic $n$-component spin models by expanding in powers of $\frac{1}{n}$ has been very helpful in studying static critical phenomena. The limit $n\to \infty$ is the spherical model. There are many possible generalizations of these models for studying dynamic (time dependent) critical phenomena. In this paper we study the propagation of sound waves and heat diffusion near the critical point in a $\frac{n}{2}$- component complex-spin (each complex component has two real components) model in the limit of large $n$. This model is a particular dynamic generalization of the spherical model and is equivalent to a system of bosons obeying quantum mechanics.