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Generalised Master Equation for the Spin‐Boson Hamiltonian by the Projection Operator Technique
Author(s) -
Cheche T. O.,
Hayashi M.,
Lin S. H.
Publication year - 2000
Publication title -
journal of the chinese chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 45
eISSN - 2192-6549
pISSN - 0009-4536
DOI - 10.1002/jccs.200000100
Subject(s) - master equation , hamiltonian (control theory) , operator (biology) , boson , quantum master equation , rotating wave approximation , bloch equations , mathematical physics , quantum , quantum mechanics , statistical physics , chemistry , physics , mathematics , mathematical optimization , biochemistry , repressor , transcription factor , gene
Starting from the von Neuman equation of quantum theoretical dynamics, by using the projection operator technique, we write the generalised master equation (GME) of the reduced statistical operator. By using this technique we find a series expansion of the memory kernel which allows, in principle, a treatment of the higher orders of approximation. By keeping only the first term of this expansion, which corresponds to the second order of the perturbation treatment, GME is applied, in the Markov approximation, to the spin boson Hamiltonian to describe the dynamics of the relevant pseudo‐spin subsystem. In the secular and rotating wave approximations this dynamics is found to be described by the Bloch equations.