Abstract
Memory effects in open quantum dynamics are often incorporated in the equation of motion through a superoperator known as the memory kernel, which encodes how past states affect future dynamics. However, the usual prescription for determining the memory kernel requires information about the underlying system-environment dynamics. Here, by deriving the transfer tensor method from first principles, we show how a memory kernel master equation, for any quantum process, can be entirely expressed in terms of a family of completely positive dynamical maps. These can be reconstructed through quantum process tomography on the system alone, either experimentally or numerically, and the resulting equation of motion is equivalent to a generalised Nakajima-Zwanzig equation. For experimental settings, we give a full prescription for the reconstruction procedure, rendering the memory kernel operational. When simulation of an open system is the goal, we show how our procedure yields a considerable advantage for numerically calculating dynamics, even when the system is arbitrarily periodically (or transiently) driven or initially correlated with its environment. Namely, we show that the long time dynamics can be efficiently obtained from a set of reconstructed maps over a much shorter time.
Highlights
In this Article, we start by solving this problem definitively: First, in Sec. 2 we derive transfer tensors from first principles for any open quantum dynamics, in particular those with initial correlations and generators that have arbitrary periodic or transient time dependence
There will be choices of σt such that ρEt0 is a stationary state with respect to LEt, leading to time-independent projectors PSE and QSE. In this Article, we have presented a derivation of the transfer tensor method, leading to a scheme for relating an operationally meaningful description of any open quantum process, in terms of completely positive dynamical maps, to a Nakajima-Zwanzig equation that depends on the underlying systemenvironment dynamics
In addition to providing a fundamental connection between two different pictures of open dynamics, our result opens up the possibility for efficient simulation of the long-time evolution of driven systems or those with initial correlations
Summary
A large fraction of active research in physics and chemistry, both theoretical and experimental, involves characterising or modelling the dynamics of. Unless the underlying dynamics is homogeneous in time, and the system is initially uncorrelated with its environment, there is no clear way to construct the memory kernel or transfer tensors operationally, either in experiment or in numerical simulations In this Article, we start by solving this problem definitively: First, in Sec. 2 we derive transfer tensors from first principles for any open quantum dynamics, in particular those with initial correlations and generators that have arbitrary periodic or transient time dependence. Given a microscopic description, to cast any open dynamics in the form of Eq (2) using the Nakajima-Zwanzig projection superoperator technique [6] (see Sec. 4 and Appendix D), though the solution of the resulting equation is far from trivial and calculating the memory kernel for different models remains an ongoing
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