Quantum dynamics with quantum Boltzmann statistics: simulations of liquid water and ice

In water and ice, the atomic nuclei exhibit quantum properties, which a growing body of evidence suggests are caused almost entirely by the quantum Boltzmann statistics, with the dynamics of the nuclei being classical. Here we summarise a recently developed theory which explains how such a classical dynamics can arise as a result of certain properties of the quantum statistics. This dynamics involves the motion of smooth delocalised loops of the hydrogen atoms which, despite being classical, conserve the quantum Boltzmann distribution. Exact implementation of this dynamics is not possible because of a phase problem, but its approximate implementation can be done using mean-field and ‘planetary’ methods. We report recent applications of these methods to simulations of the infrared spectrum of liquid water and ice.