Proton Tunneling Relaxation in the Dielectric glass RADP

Tunneling plays an important role in glassy relaxation at low temperature, but quantitative modeling of data is rare. We relate the dielectric susceptibility over 7 decades of frequency to the microscopic hydrogen free energy landscape obtained in neutron Compton experiments for the proton glass Rb$_{0.28}$(NH4)$_{0.72}$H$_{2}$PO$_{4}$ (RADP:72). RADP is a dipolar structural glass with spatial frustration between local ferroelectric RDP and antiferroelectric ADP ordering. We find a well-defined attempt frequency and a logarithmic relaxation over decades of frequency, with a classical to quantum crossover analogous to the vortex tunneling dynamics in high T$_{c}$ superconductors.