First-Principles Simulation of Nonequilibrium Coupled Electron–Phonon Dynamics: Algorithms, Acceleration, and Coherent Phenomena

Author: Yao, Jia (Kelly)

Year: 2026

Degree: Dissertation (Ph.D.)

Advisor: Bernardi, Marco

Committee Members: Hsieh, David; Cushing, Scott K.; Refael, Gil; Bernardi, Marco

Option: Physics

DOI: 10.7907/pw5b-ge31

Abstract

Studying nonequilibrium charge and heat transport is central to the design and control of modern electronic, optoelectronic, and energy materials. On ultrafast timescales, these processes, such as carrier relaxation, lattice heating, and lattice-driven changes of material properties are governed by coupled electron-phonon dynamics. While first-principles methods based on density functional theory enable quantitative predictions of electron-phonon and phonon-phonon (ph-ph) \mbox{interactions}, their extension to real-time, fully coupled nonequilibrium simulations remains computationally challenging, particularly for complex materials and long simulation times.

This thesis develops and advances a comprehensive first-principles framework for simulating nonequilibrium coupled electron-phonon dynamics within the real-time Boltzmann transport equation (rt-BTE). Several algorithmic and computational strategies are introduced to overcome the prohibitive cost of such simulations. First, adaptive and multirate time-integration schemes are developed to efficiently resolve disparate electronic and phononic timescales, enabling accurate simulations of coupled dynamics in complex materials with anharmonic ph-ph interactions. Second, dynamic mode decomposition is applied to extrapolate long-time behavior from short-time simulations, providing efficient access to steady-state and transient transport regimes. Third, GPU parallelization and algorithm optimization are implemented to accelerate the evaluation of collision integrals, yielding substantial performance improvements on modern high-performance computing architectures. Fourth, tensor-learning and compression techniques are introduced to reduce the computational and memory costs associated with ph-ph interactions, further enabling simulations previously inaccessible due to system size or interaction complexity.

Beyond algorithmic acceleration, this work extends the theoretical description of nonequilibrium lattice dynamics from the rt-BTE by introducing a framework accounting for coherently driven phonon dynamics, bridging the gap between incoherent transport and coherent ultrafast phenomena observed in modern pump-probe experiments. Together, these developments expand the efficiency and scope of first-principles simulations of nonequilibrium electron-phonon dynamics, providing new tools for studying transport, relaxation, and coherent control in quantum materials.

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