Abstract
The dynamic behavior of a system undergoing a cooperative Jahn-Teller structural transition is investigated. Coupling to both acoustic and optic modes are considered. Particular emphasis is placed on the low-frequency response. In addition to the peaks in the dynamic structure factor corresponding to the soft acoustic mode, a central component is obtained, the width of which goes to zero as the transition temperature is approached. Unlike other transitions for which a central component has been observed, the width of the central peak for Jahn-Teller transitions such as that in TmV${\mathrm{O}}_{4}$ may be sufficiently wide to allow a direct observation of the narrowing by neutron scattering or other techniques.
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