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, or IS), sampled over a wide range of
temperatures and volumes, the ring-polymers are collapsed. This considerably
facilitates the description of quantum liquids using the PEL formalism.
Specifically, the normal modes of the ring-polymer system/quantum
liquid at an IS 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).