Post-Markovian master equation \`{a} la microscopic collisional model

TL;DR

This paper introduces a new post-Markovian master equation derived from microscopic collisional models, capable of capturing a wide range of open quantum system dynamics and accelerating thermalization processes.

Contribution

It presents a completely positive, analytically solvable post-Markovian master equation derived from microscopic models, bridging Markovian and non-Markovian dynamics.

Findings

The PMME can reduce to Nakajima-Zwanzig or Markovian equations.

Post-Markovian dynamics accelerate thermalization.

The approach demonstrates collisional models' versatility in simulating open quantum systems.

Abstract

We derive a completely positive post-Markovian master equation (PMME) from a microscopic Markovian collisional model framework, incorporating bath memory effects via a probabilistic single-shot measurement approach. This phenomenological master equation is both analytically solvable and numerically tractable. Depending on the choice of the memory kernel function, the PMME can be reduced to the exact Nakajima-Zwanzig equation or the Markovian master equation, enabling a broad spectrum of dynamical behaviors. We also investigate thermalization using the derived equation, revealing that the post-Markovian dynamics accelerates the thermalization process, exceeding rates observed within the Markovian framework. Our approach solidifies the assertion that "collisional models can simulate any open quantum dynamics", underscoring the versatility of the models in realizing open quantum systems.