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Master equation
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== Quantum master equations == A [[quantum master equation]] is a generalization of the idea of a master equation. Rather than just a system of differential equations for a set of probabilities (which only constitutes the diagonal elements of a [[density matrix]]), quantum master equations are differential equations for the entire density matrix, including off-diagonal elements. A density matrix with only diagonal elements can be modeled as a classical random process, therefore such an "ordinary" master equation is considered classical. Off-diagonal elements represent [[quantum coherence]] which is a physical characteristic that is intrinsically quantum mechanical. The [[Redfield equation]] and [[Lindblad equation]] are examples of approximate [[quantum master equation]]s assumed to be [[Markov process|Markovian]]. More accurate quantum master equations for certain applications include the polaron transformed quantum master equation, and the [[VPQME]] (variational polaron transformed quantum master equation).<ref name=McCutcheon>{{cite journal |last1=McCutcheon |first1=D. |last2=Dattani |first2=N. S. |last3=Gauger |first3=E. |last4=Lovett |first4=B. |last5=Nazir |first5=A. |date=25 August 2011 |title=A general approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots |journal=Physical Review B |volume=84 |issue=8 |page=081305R |doi=10.1103/PhysRevB.84.081305 |arxiv = 1105.6015 |bibcode=2011PhRvB..84h1305M|hdl=10044/1/12822 |s2cid=119275166 }}</ref>
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