Dissertations, Theses, and Capstone Projects

Date of Degree

9-2026

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy

Program

Physics

Advisor

Nicolas Giovambattista

Committee Members

Johannes Flick

Gustavo E. Lopez

Peter H. Poole

Karl Sandeman

Subject Categories

Quantum Physics | Statistical, Nonlinear, and Soft Matter Physics

Abstract

Atomic delocalization due to nuclear quantum effects (NQE) remains poorly understood in low-temperature liquids near the glass state and during vitrification. Many liquids can be described accurately by treating their nuclei as classical particles, but this approximation fails for light elements such as He and H₂, small hydrogen-containing molecules such as water, and systems in which zero-point motion or isotope-substitution effects are important. Developing a general thermodynamic and statistical-mechanical description of such liquids has been challenging. This dissertation extends the potential energy landscape (PEL) formalism, originally developed for classical liquids and glasses, to liquids that obey quantum mechanics and exhibit relevant NQE. The PEL formalism expresses the canonical partition function in terms of the topography of the system's potential energy surface, including its local minima (inherent structures, IS), the distribution of IS energies, and the curvature about the IS. The path-integral formulation of statistical mechanics maps the canonical partition function of a quantum liquid onto that of a classical ring-polymer system. Applying the PEL formalism to the potential energy surface of this ring-polymer system provides a thermodynamic description of the quantum liquid. The resulting quantum PEL is temperature-dependent, unlike its classical counterpart, and therefore requires modified PEL expressions. Across the atomistic liquids studied here, the Gaussian approximation describes the PEL in the relevant regimes, and the ring polymers collapse at the corresponding IS. Under these conditions, the IS of the ring-polymer system are in one-to-one correspondence with those of the classical liquid counterpart, substantially simplifying the quantum PEL formalism. We apply this formalism to ask how quantum fluctuations affect the glass transition of atomistic liquids. Previous studies showed that weak or moderate NQE slow the dynamics of a Lennard–Jones binary mixture, whereas very large delocalization restores the expected increase in dynamics. Our path-integral simulations show that this behavior is not universal: in the water-like Fermi–Jagla liquid, dynamics instead increase monotonically with NQE. Atomic delocalization and pair structure alone do not explain this contrast, which can be interpreted using the different PEL regions and basin shapes sampled by the two liquids. Finally, we extend the PEL formalism from ring polymers with a finite number of beads to the continuous limit, n_b → ∞. The principal PEL properties converge in this limit; within the harmonic and Gaussian approximations, the Helmholtz free energy of the quantum liquid can be obtained using classical molecular dynamics simulations rather than path-integral simulations. Overall, the PEL formalism provides a common statistical-mechanical framework for the thermodynamic and dynamical properties of classical and quantum liquids that obey Maxwell–Boltzmann statistics. Its extension to quantum statistics and bosonic systems is discussed briefly as a future direction.

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