We discuss a simplified version of an ice lattice which consists of an alternating sequence of heavy and light masses. The light masses (protons) are each subject to a bistable potential caused by the heavy masses (oxygens). The protons interact with one another, as do the heavy ions. The interactions between the protons and the oxygens modulate the bistable proton potential. This system is known to exhibit kink and antikink solutions associated with mobile ionic defects accompanied by a lattice distortion. We show that at finite temperatures and in the presence of a constant external field on the protons, the defect velocity is a nonmonotonic function of the temperature, reflecting an interesting interplay of thermal effects (noise) and the constant deterministic external forcing in this nonlinear system. We discuss extensions of the model to higher dimensions, and present preliminary results for the proton motion in such networks.
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Nylund, E., Lindenberg, K. & Tsironis, G. Proton dynamics in hydrogen-bonded systems. J Stat Phys 70, 163–181 (1993). https://doi.org/10.1007/BF01053961
- Hydrogen-bonded networks
- proton dynamics
- multidimensional effects
- collective motion