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Register a new userNote: Nonuniqueness of generalized quantum master equations for a single observable
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When deriving exact generalized master equations for the evolution of a reduced set of degrees of freedom, one is free to choose what quantities are relevant by specifying projection operators. Different choices of projectors can lead to master equations that are structurally dissimilar and have different memory kernels, despite the resulting dynamics being necessarily the same. This owes to the interplay between projections and explicit imposition of dynamical constraints. We give a simple example to show this point and prove how different memory kernels can yield the same dynamics.
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We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes, and puts into evidence the non uniqueness of the relationship arising due to the typical quantum issue of operator ordering. The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory description of the dynamics. Previous apparently unrelated results are now connected in a unified framework, which further allows to phenomenologically construct a large class of non-Markovian evolutions taking as starting point collections of time dependent maps and instantaneous transformations describing the microscopic interaction dynamics.
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