Algebraic Structure of a Master Equation with Generalized Lindblad Form
Kazuyuki Fujii (Yokohama City University)
TL;DR
This paper explores the algebraic structure of a generalized Lindblad master equation for quantum systems, extending previous solutions for the damped harmonic oscillator by utilizing Lie algebra representations and constructing approximate solutions.
Contribution
It introduces a generalized Lindblad form for master equations and analyzes the associated Lie algebra structures, providing new methods for approximate solutions.
Findings
Identified algebraic structures related to Lie algebras in generalized Lindblad equations
Constructed an approximate solution for the generalized master equation
Extended previous solutions from specific to more general quantum damping models
Abstract
The quantum damped harmonic oscillator is described by the master equation with usual Lindblad form. The equation has been solved completely by us in arXiv : 0710.2724 [quant-ph]. To construct the general solution a few facts of representation theory based on the Lie algebra were used. In this paper we treat a general model described by a master equation with generalized Lindblad form. Then we examine the algebraic structure related to some Lie algebras and construct the interesting approximate solution.
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