Symmetry analysis and algebraic structures of the Hu-Paz-Zhang Master Equation
Richard M. Morris, Peter G.L. Leach
TL;DR
This paper uses Lie symmetry analysis to explore the algebraic structures of the Hu-Paz-Zhang Master Equation, which models a harmonic oscillator interacting with a heat bath, focusing on constant parameters.
Contribution
It applies Lie group theory to analyze symmetries of the Hu-Paz-Zhang Master Equation, revealing its algebraic structure and potential solution methods.
Findings
Identified symmetry groups of the equation
Classified algebraic structures related to the equation
Provided insights into solution techniques for the model
Abstract
We apply the Lie Theory of continuous groups to investigate the symmetries of the Hu-Paz-Zhang Master Equation which arises in the modelling of the interaction of a harmonic oscillator with a linear passive heat bath of oscillators. We examine the case in which the parameters of the equation are constant.
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Taxonomy
TopicsNonlinear Photonic Systems · Nonlinear Waves and Solitons · Nonlinear Dynamics and Pattern Formation