Potential Energy Landscape Formalism for Quantum Liquids

The potential energy landscape (PEL) formalism is a theoretical approach within statistical mechanics used extensively in the past to study classical liquids and glasses. Here, we extend the PEL formalism to the case of quantum liquids. As an example, we apply the PEL approach to study a family of quantum monatomic liquids using path-integral Monte Carlo simulations. We focus on the energy (E_IS), pressure (P_IS) of the local minima of the PEL (inherent structures, IS) explored by the liquids. We find that, similar to the classical case, the quantum liquids exhibit a PEL-independent regime at high temperatures and a PEL-influenced regime at low temperatures, where the topography of the PEL plays a major role. Remarkably, the ring-polymers representing the atoms of the quantum liquids are collapsed at the IS. Accordingly, an IS of the quantum liquid, in its own PEL, is also an IS of the classical liquid in the classical liquid PEL (CL-PEL). A pictorial interpretation of the behavior of quantum liquids using the CL-PEL (as opposite of the quantum liquid PEL) is provided. In this approach, the quantum liquid is represented by a pancake-like patch that expands over multiple IS of the CL-PEL, changing shape with time while describing a fuzzy trajectory on the CL-PEL