# Coherent backaction between spins and an electronic bath: Non-Markovian dynamics and low-temperature quantum thermodynamic electron cooling

## TL;DR

This paper develops an analytical framework to model non-Markovian spin dynamics in contact with an electronic bath, revealing full decay behavior and proposing a quantum thermodynamic cooling scheme for electrons at low temperatures.

## Contribution

It introduces a systematic method to analyze non-Markovian spin-bath interactions, extending beyond traditional Markovian approximations, and proposes a novel electron cooling technique.

## Key findings

- Full analytic description of spin decay from non-Markovian to exponential regimes
- Demonstration of temperature-insensitive decay useful for cooling
- Proposal of a spin-based scheme to cool electrons at very low temperatures

## Abstract

We provide a versatile analytical framework for calculating the dynamics of a spin system in contact with a fermionic bath beyond the Markov approximation. The approach is based on a second order expansion of the Nakajima-Zwanzig master equation but systematically includes all quantum coherent memory effects leading to non-Markovian dynamics. Our results describe, for the free induction decay, the full time range from the non-Markovian dynamics at short times, to the well-known exponential thermal decay at long times. We provide full analytic results for the entire time range using a bath of itinerant electrons as an archetype for universal quantum fluctuations. Furthermore, we propose a quantum thermodynamic scheme to employ the temperature insensitivity of the non-Markovian decay to transport heat out of the electron system and thus, by repeated reinitialization of a cluster of spins, to efficiently cool the electrons at very low temperatures.