Potential energy landscape formalism for quantum liquids

Abstract

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 (EIS) and pressure (PIS) of the local minima of the PEL [inherent structures (IS)] explored by the liquids. It is found 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. Interestingly, the PEL of all the quantum liquids studied is Gaussian, providing a simple expression for the configurational entropy of the liquids. 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 to the quantum liquid PEL) is provided. In this view, the quantum liquid is represented by a pancakelike patch that expands over multiple IS of the CL-PEL, changing shape with time while describing a fuzzy trajectory (on the CL-PEL). The formalism described in this work is general and can, in principle, be extended to quantum systems other than liquids.