Extension of the Nakajima-Zwanzig approach to multitime correlation functions of open systems

Abstract

We extend the Nakajima-Zwanzig projection operator technique to the determination of multitime correlation functions of open quantum systems. The correlation functions are expressed in terms of certain multitime homogeneous and inhomogeneous memory kernels for which suitable equations of motion are derived. We show that under the condition of finite memory times these equations can be used to determine the memory kernels by employing an exact stochastic unraveling of the full systemenvironment dynamics. The approach thus allows to combine exact stochastic methods, feasible for short times, with long-time master equation simulations. The applicability of the method is demonstrated by numerical simulations of 2D-spectra for a donor-acceptor model, and by comparison of the results with those obtained from the reduced hierarchy equations of motion. We further show that the formalism is also applicable to the time evolution of a periodically driven two-level system initially in equilibrium with its environment.

Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics

“…Despite this difficulty, recent work has generalized the NZ equation to multi-time correlation functions. 42 In contrast, the more flexible Mori formulation permits direct extension to multipletime and equilibrium correlation functions, which are essential in the treatment of linear 43 and non-linear spectroscopy, 44 and the calculation of chemical rate constants 21,45 and kinetic coefficients, 46 to name a few examples. For this reason, in paper I (this paper) of this series, we provide a unified Mori-type framework to approach single-time nonequilibrium correlation functions, and address several of the open questions listed above.…”

Quantum Foundations of Classical Reversible Computing

“…In the specific case thatL is independent of time, this simplifies to ρ(t) = e tL ρ(t 0 ). In general, this may not be guaranteed to converge, let alone have a closed-form solution [72][73][74]. 27 Nevertheless, this is the formal solution to the LvN equation (56).…”

Discrete memory kernel for multitime correlations in non-Markovian quantum processes

“…In this paper, we develop a generalization of the transfertensor formalism to a scenario involving sequential measurements of a non-Markovian open system as it evolves, resulting in an efficient discrete-time memory kernel method for the propagation of multitime correlation functions. In contrast to previous multitime memory kernel methods, for which correlations between each set of operators require a separate kernel [28], our approach utilizes the powerful process-tensor formalism to encode all correlations of a given order into a single positive operator [16,29]. As an illustration of the utility of our generalized method, we study the buildup of system-environment correlations in the paradigmatic spin-boson model and compute steady-state emission spectra, taking into account system-environment correlations present in the steady state.…”