# A hybrid memory kernel approach for condensed phase non-adiabatic dynamics

## TL;DR

This paper introduces a hybrid memory kernel method for non-adiabatic dynamics in condensed phase systems, combining exact slow-bath solutions with NIBA to improve accuracy in challenging regimes.

## Contribution

It develops a hybrid approach that enhances second-order methods with higher-order effects, improving dynamics predictions for complex systems.

## Key findings

- The hybrid kernel outperforms NIBA in large diabatic coupling regimes.
- The method maintains computational efficiency similar to NIBA.
- It provides an exact solution in the slow-bath limit and effective approximations for faster baths.

## Abstract

The spin-boson model is a simplified Hamiltonian often used to study non-adiabatic dynamics in large condensed phase systems, even though it has not been solved in a fully analytic fashion. Herein, we present an exact analytic expression for the dynamics of the spin-boson model in the infinitely slow bath limit and generalize it to approximate dynamics for faster baths. We achieve the latter by developing a hybrid approach that combines the exact slow-bath result with the popular NIBA method to generate a memory kernel that is formally exact to second order in the diabatic coupling but also contains higher-order contributions approximated from the second order term alone. This kernel has the same computational complexity as NIBA, but is found to yield dramatically superior dynamics in regimes where NIBA breaks down---such as systems with large diabatic coupling or energy bias. This indicates that this hybrid approach could be used to cheaply incorporate higher order effects into second order methods, and could potentially be generalized to develop alternate kernel resummation schemes.