School of Physics Thesis Dissertation Defense

Elyana Crowder Melnick 
Advisor: Dr. Dragomir Davidović, School of Physics, Georgia Institute of Technology

Higher Order Perturbative Quantum Master Equations
Date: Friday, April 4th, 2025 
Time: 9:00 a.m.  
Location: Howey Physics Building, Room W401
Zoom Link: https://gatech.zoom.us/j/94022682974?pwd=OuagAa3ybYS1jW46LlqAKUe9FYGYHa…
Meeting ID: 940 2268 2974
Passcode: 774314

Committee Members:
Dr. Brian Kennedy, School of Physics, Georgia Institute of Technology
Dr. Itamar Kimchi, School of Physics, Georgia Institute of Technology
Dr. Michael Loss, School of Mathematics, Georgia Institute of Technology
Dr. Zhu-Xi Luo, School of Physics, Georgia Institute of Technology

Abstract: 
Perturbative master equations are useful for modeling how an open quantum system evolves in contrast with its isolated counterpart. The Time Convolutionless Master Equation (TCL) is exact, and the generator can be expanded in orders of the system-environment coupling strength λ and account for non-Markovian dynamics while remaining a time-local equation. However, terms of the perturbative order λN Time Convolutionless equation (TCLN) past N=2, are notably difficult to compute for general systems since they require the evaluation of N−1 nested integrals, limiting their usability. Motivated by the necessity of the TCL4 generator to model asymptotic states to the first nonzero order in the interaction, this dissertation presents a simplified form of TCL4 where the triple integrals are reduced to a single integral over terms optimized for numeric evaluation.
This simplified TCL4 generator enables the identification of infrared (frequency ® zero) divergences in the long-time limit, dependent on the power-law scaling of the bath spectral density, s. For the s < 1 case (sub-ohmic bath), results show that though the generator converges at second order in the long-time limit, the fourth order contribution can diverge, constraining the range of validity of previous solutions. Applying the same simplification steps to the TCL6 generator, collaborative results indicate that in general the N−1 integrals can be reduced to ⌊N/2⌋−1. Additionally, there is a maximum N after which infrared divergences can appear for all finite s. Further analysis shows that resolving the infrared divergences through a resummed TCL master equation (rTCL) results in new inflationary terms at finite nonzero frequency. Physical interpretation of these divergences will be the focus of future study.