# Towards generic adiabatic elimination for bipartite open quantum systems

## TL;DR

This paper develops a systematic adiabatic elimination method for bipartite open quantum systems, allowing derivation of reduced models that accurately describe slow subsystem dynamics with explicit second-order formulas.

## Contribution

It introduces a general adiabatic elimination technique for bipartite open quantum systems using asymptotic expansion and geometric singular perturbation theory, ensuring physical consistency.

## Key findings

- Derived explicit second-order formulas for reduced dynamics.
- Ensured the reduced model is in Lindblad form.
- Provided formulas for Hamiltonian and cascade couplings.

## Abstract

We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the time-scale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow subsystem. The method, based on an asymptotic expansion and geometric singular perturbation theory, ensures the physical interpretation of the reduced second-order model by giving the reduced dynamics in a Lindblad form and the state reduction in Kraus map form. We give explicit second-order formulas for Hamiltonian or cascade coupling between the two subsystems. These formulas can be used to engineer, via a careful choice of the fast subsystem, the Hamiltonian and Lindbald operators governing the dissipative dynamics of the slow subsystem.