Non-equilibrium Dynamics of Interacting Tunneling States in Glasses

After the temporary application of a strong electric bias field to a glass sample at temperatures in the milli-Kelvin range its dielectric constant is increased and then decays slowly back to its equilibrium value. We studied these dielectric non-equilibrium properties of the polyester glass Mylar and the borosilicate glass BK7 as a function of bias field and temperature. We find that the decay to equilibrium depends on the duration of the applied bias field substantially only if the sample has been biased for several thousand seconds or longer. The decay curves after shorter bias field applications are influenced rather by the rate by which the field has been changed. Following the ”dipole gap” theory1 we assume that the observed excess dielectric response originates in the non-equilibrium dynamics of tunneling states (TSs) that are strongly coupled. Our analysis of the data within the framework of strongly coupled pairs of TSs indicates three competing equilibrium destroying processes, leading to the observed dynamics. Obviously the energy relaxation rate of TSs depends on the bias field since it changes the energy splitting of TSs by coupling to their dipole moments. In addition, a quick enough field sweep can drive TSs non-adiabatically between their energy eigen-states yielding sweep rate dependent decay times. The third process results in decay times independent of temperature and the bias field sweep rate and duration. We propose a picture where the field lifts the tunneling particle in potential wells beyond its original double well as the cause of the third contribution. The decay towards equilibrium is by quantum mechanical tunneling. Moreover, our observations indicate that below a material dependent temperature the relaxation of TSs is caused primarily by interactions between them.