Quantum acoustics of the Jahn-Teller complexes in doped crystals: Configurational relaxation time as indicator of the complex

Experiments carried out with the use of ultrasonic technique in doped crystals have established three mechanisms of relaxation of the Jahn-Teller subsystem at low temperatures. All of them have a quantum nature. The Debye relaxation function $f_D=1/(1+i\omega \tau )$ is changed due to the temperature-dependent relaxation time $\tau \left(T\right)$ provided the frequency $\omega$ is fixed. The dependence of $\tau \left(T\right)$ derived in an experiment on dissipation or/and dispersion of an ultrasonic wave makes it possible to obtain the temperature dependence of $f_D\left(T\right)$. As a consequence of quantum nature of the relaxation mechanisms, the dependence of $\tau \left(T\right)$ at low temperatures is an immanent characteristic of the system of Jahn-Teller complexes in a given matrix. Therefore graphical representations of $-\mathrm{Im}{f}_D\left(T\right)$ and $-\mathrm{Im}{f}_D\left(T\right)/T$ can serve as fingerprints of a certain Jahn-Teller complex.