The Harmonic and Gaussian Approximations in the Potential Energy Landscape Formalism for Quantum Liquids

The potential energy landscape (PEL) formalism has been used in the past to describe the behavior of classical low-temperature liquids and glasses. Here, we extend the PEL formalism to describe the behavior of liquids and glasses that obey quantum mechanics. In particular, we focus on the (i) harmonic and (ii) Gaussian approximations of the PEL, which have been commonly used to describe classical systems, and show how these approximations can be applied to quantum liquids/glasses. Contrary to the case of classical liquids/glasses, the PEL of quantum liquids is temperature-dependent and hence, the main expressions resulting from approximations (i) and (ii) depend on the nature (classical vs. quantum) of the system. The resulting theoretical expressions from the PEL formalism are compared with results from path-integral Monte Carlo (PIMC) simulations of a monatomic model liquid. In the PIMC simulations, every atom of the quantum liquid is represented by a ring-polymer. Our PIMC simulations show that, at the local minima of the PEL (inherent structures), sampled over a wide range of temperatures and volumes, the ring-polymers are collapsed. This facilitates considerably the description of quantum liquids using the PEL formalism. Specifically, the normal modes of the quantum liquid can be calculated analytically if the normal modes of the classical liquid counterpart are known (as obtained, e.g., from classical MC or molecular dynamics simulations of the corresponding atomic liquid).