Mechanical and Civil Engineering Seminar

Ph.D. Thesis Defense

Abstract:

Three different computational many-body physics problems are considered. First is to compute the cross-plane thermal conductivity of 1-D superlattices using the Boltzmann transport equation (BTE) with material parameters obtained from ab-initio calculations. Symmetries are incorporated to make this computation more manageable. We verify that the BTE is unable to reproduce a trend in superlattice thermal conductivity observed in recent experiments [1], suggesting that it is indicative of wave-like phonon behavior. Second is to investigate using a low-rank representation of the electronic structure Hamiltonian in quantum computing algorithms. In our representation of the Hamiltonian, implementing a Trotter step is expected to have O(N^4) computational complexity. We find that allowing for low-rank approximations should allow one to reduce the complexity to O(N^3). Third is to obtain the long-time dynamics of single-site observables for general quantum systems. We achieve this by using matrix product states (MPS) algorithms to compute and represent a low-rank approximation of the influence functional. We find that this method can be used to compute dynamics for longer times than traditional tensor network methods.

[1] J. Ravichandran, et al. Crossover from incoherent to coherent phonon scattering in epitaxial oxide superlattices. Nature Mater. 13, 168–172 (2014)

Please virtually attend this thesis defense:

Zoom Link: https://caltech.zoom.us/j/89592501247