Lindblad approximation and spin relaxation in quantum electrodynamics

TL;DR

This paper derives a Lindblad approximation for the spin dynamics of a 1/2-spin particle in a magnetic field coupled to quantized photons, with uniform error bounds in time.

Contribution

It provides a rigorous derivation of a Lindblad-type equation for spin relaxation with explicit error bounds uniform in time.

Findings

Lindblad approximation accurately models spin dynamics.

Error bound of order g^2 is established.

Uniform in time error control is achieved.

Abstract

This article is concerned with the time evolution of a $\frac{1}{2}$-spin particle in a constant external magnetic field with the quantized electromagnetic field (photons). We derive a Lindblad (or GKLS) type approximation of the spin dynamics together with a precise control of the error coming from this approximation. The error term is bounded by $g^2$ where $g$ is the coupling constant of the spin-photon interaction. The point here is the uniformity in time $t>0$ of this error control.