In partial fulfillment of the requirements for the degree of 

Doctor of Philosophy in Physics 

School of Physics Dissertation Defense

Jiahao Chen
Dr. Dragomir Davidovic, School of Physics, Georgia Institute of Technology (Advisor)

Numerical Approach to the Time-Convolutionless (TCL) Master Equation

Date: Tuesday, November 10, 2026
Time: 8:30 a.m. EST
Location: Howey N201/202
Virtual: Join the Microsoft Teams meeting / Meeting ID: 273 524 787 663 512 4 / Passcode: ub6Fd2TB

Thesis Committee:

Dr. Brian Kennedy, School of Physics, Georgia Institute of Technology

Dr. Martin Mourigal, School of Physics, Georgia Institute of Technology

Dr. Xueda Wen, School of Physics, Georgia Institute of Technology

Dr. Qi Tang, School of Computational Science and Engineering, Georgia Institute of Technology

Abstract:

Open quantum systems are quantum systems that interact with their environment. The time-convolutionless (TCL) master equation provides a formally exact, time-local description of their dynamics. However, the computational cost of evaluating higher-order terms often limits practical applications to the second-order approximation. We develop systematic numerical methods that reduce the temporal complexity to O(N log N) for TCL4 and O(N log² N) for TCL6, where N is the number of time points. We extend the construction to higher orders and assess its accuracy using spin–boson benchmarks. We also investigate the convergence limits of the TCL expansion and explore resummation methods for extending accurate predictions beyond direct perturbative truncation.