52 research outputs found
Nature and origin of the operators entering the master equation of an open quantum system
By exploiting the peculiarities of a recently introduced formalism for
describing open quantum systems (the Parametric Representation with
Environmental Coherent States) we derive an equation of motion for the reduced
density operator of an open quantum system that has the same structure of the
celebrated Gorini-Kossakowski-Sudarshan-Lindblad equation, but holds regardless
of markovianity being assumed. The operators in our result have explicit
expressions in terms of the Hamiltonian describing the interactions with the
environment, and can be computed once a specific model is considered. We find
that, instead of a single set of Lindblad operators, in the general
(non-markovian) case there one set of Lindblad-like operators for each and
every point of a symplectic manifold associated to the environment. This
intricacy disappears under some assumptions (which are related to markovianity
and the classical limit of the environment), under which it is possible to
recover the usual master equation formalism. Finally, we find such
Lindblad-like operators for two different models of a qubit in a bosonic
environment, and show that in the classical limit of the environment their
renown master equations are recovered.Comment: 19 pages, 1 figur
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