Time-Convolutionless Master Equation Applied to Adiabatic Elimination

TL;DR

This paper reformulates adiabatic elimination in open quantum systems using the time-convolutionless master equation, providing a practical, accessible approach that bridges existing methods and offers new insights into complex quantum dynamics.

Contribution

It introduces a TCL master equation framework for adiabatic elimination, connecting geometric and algebraic approaches and expanding applicability to complex systems.

Findings

TCL formulation yields results equivalent to geometric approach

Demonstrates practical methodology with typical examples

Provides a geometric interpretation of TCL formalism

Abstract

In open quantum systems theory, reduced models are invaluable for conceptual understanding and computational efficiency. Adiabatic elimination is a useful model reduction method for systems with separated timescales, where a reduced model is derived by discarding rapidly decaying degrees of freedom. So far, adiabatic elimination has been formulated using a geometric approach, which provides a versatile and general framework. This article introduces a reformulation of adiabatic elimination through the framework of the time-convolutionless (TCL) master equation, a widely recognized tool for computing projected time evolution in open quantum systems. We show that the TCL master equation formulation yields results equivalent to those obtained from the geometric formulation. By applying the TCL master equation formulation to typical examples, we demonstrate a practical methodology for performing adiabatic elimination calculation. This study not only bridges two previously independent approaches, thereby making the adiabatic elimination method accessible to a broader audience, but also enables the analysis of complex cases that are challenging within the geometric formulation. Additionally, it reveals a geometric interpretation of the TCL master equation formalism.