GEOMETRIC PHASE EMERGENT FROM COLLECTIVE ATOMIC MOTION IN HYDROGEN-BONDED ICE, BIOMOLECULES, AND FERROELECTRICS

We propose here the existence of Berry's phase in hydrogen-bonded ice. We find dramatic effects of the geometric phase when it exists in a s ystem having many equivalent potential wells with moderate barriers be tween them. Energy level splitting of ground states by tunneling is su ppressed by the geometric phase and the degeneracy of the ground state s increases enormously, leading to the macroscopically observable resi dual (zero-point) entropy as experimentally measured in crystalline ic e. This novel understanding of the residual entropy replaces the class ical configuration-counting argument and sheds new light on the limit of the third law of the thermodynamics in quantum mechanical setting. Furthermore, in the presence of small perturbing potentials in the hyd rogen-bonded water, biomolecules, and ferroelectrics, the degeneracy i s shown to be lifted to give rise to very low energy excitations.