We use basic physical motivations to develop sufficient conditions for positive semidefiniteness of the reduced density matrix for generalized non-Markovian integrodifferential Lindblad–Kossakowski master equations with Hermitian generators. We show that it is sufficient for the memory function to be the Fourier transform of a real positive symmetric frequency density function with certain properties. These requirements are physically motivated, and are more general and more easily checked than previously stated sufficient conditions. We also explore the decoherence dynamics numerically for some simple models using the Hadamard representation of the propagator. We show that the sufficient conditions are not necessary conditions. We also show that models exist in which the long time limit is in part determined by non-Markovian effects.

No abstract

A grid-based method for numerical solution of systems of integrodifferential dynamical equations is introduced that has computational costs which scale linearly with the grid size. Grid parameters are automatically generated from a user supplied error tolerance. We illustrate the accuracy of the method by solving a variety of representative sets of equations. The method is much faster than comparable quadratically scaling algorithms.

We show that certain positivity-preserving non-Markovian generalizations of the Kossakowski-Lindblad master equation can exhibit equilibration to an asymptotic state which is stationary with respect to the shifted system Hamiltonian for general system-bath coupling. This is in sharp contrast to results for Markovian forms which require strong relations between these operators (e.g. commutation of isolated system Hamiltonian and coupling operator). We also expand the list of sufficient conditions for positivity of non-Markovian master equations.

No abstract