Quantum and Classical Relaxation in the Proton Glass

The hydrogen-bond network formed from a crystalline solution of ferroelectric RbH_2PO_4 and antiferroelectric NH_4H_2PO_4 demonstrates glassy behavior, with proton tunneling the dominant mechanism for relaxation at low temperature. We characterize the dielectric response over seven decades of frequency and quantitatively fit the long-time relaxation by directly measuring the local potential energy landscape via neutron Compton scattering. The collective motion of protons rearranges the hydrogen bonds in the network. By analogy with vortex tunneling in superconductors, we relate the logarithmic decay of the polarization to the quantum-mechanical action.