This thesis investigates the fundamental physics and computational modeling of quantum thermal transport in crystalline systems, focusing on regimes where established theoretical approaches face intrinsic limitations. Thermal transport, studied for decades, remains an active research area due to the shrinking size and increasing complexity of materials and devices, making microscopic and mesoscopic heat propagation both a theoretical challenge and a practical necessity.
Central to this work is the study of phonons, quantized vibrational modes representing atomic oscillations in crystal lattices and primary heat carriers in insulating and semiconducting materials. Phonon scattering under temperature gradients directly impacts thermal conductivity. While first-principles simulations and semiclassical methods based on the Boltzmann transport equation and Fermi's golden rule have predictive success, they depend on approximations that fail where quantum effects and strong anharmonicity dominate.
To overcome these limitations, this thesis develops a theoretical and computational framework extending beyond conventional thermal transport models. A key focus is the breakdown of the combined Boltzmann transport equation and Fermi's golden rule in describing phonon lifetimes. By relaxing strict energy conservation in individual phonon-phonon scattering processes through collisional broadening, the approach better captures phonon interactions, especially where computational smearing creates ambiguities in thermal conductivity calculations. The work demonstrates that an accurate, consistent description requires moving beyond these approximations using Green's function theory and the full quantum Kadanoff-Baym equation. This framework inherently includes virtual phonon-mediated scattering, a quantum phenomenon always present in the quantum regime but neglected in semiclassical and current first-principles approaches, marking a significant novel contribution to computational thermal transport.
The thesis further explores heat hydrodynamics, a regime dominated by phonon collisions that conserve crystal quasi-momentum, causing phonons to flow collectively rather than diffusively, similar to real fluids. This hydrodynamic transport produces complex phenomena such as thermal backflow and phonon vortices, especially in spatially confined systems like two-dimensional materials. Analytical tools inspired by fluid dynamics are developed and applied to describe these effects, providing new insights into controlling and directing heat in mesoscale materials.
This research advances the understanding of thermal transport from both microscopic quantum dynamics and macroscopic heat flow perspectives. It enhances computational models' predictive capabilities across diverse physical conditions, offering deeper insights into phonon-mediated heat conduction and suggesting new strategies for designing materials and devices with tailored thermal properties.
