Mechanical and Civil Engineering Seminar
Reducing Computational Costs for Many-Body Physics Problems
Ph.D. Thesis Defense
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 , 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.
 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