Rigorous derivation of Lindblad equations from quantum jumps processes in 1D

TL;DR

This paper rigorously derives a Lindblad master equation for a 1D heavy particle interacting with a thermal environment via quantum jump processes, establishing a solid mathematical foundation for dissipative quantum dynamics.

Contribution

It provides the first rigorous derivation of a Lindblad equation from quantum jump processes in a 1D setting under weak coupling assumptions.

Findings

Convergence of quantum jump solutions to Lindblad equations in the weak-coupling limit

First rigorous derivation of dissipative quantum evolution equations

Establishment of a mathematical framework for quantum jumps in 1D systems

Abstract

We are interested by the behaviour of a 1D single heavy particle, interacting with an environment made of very fast particles in a thermal state. Assuming that the interactions are instantaneous, we construct an appropriate quantum jump process for the density operator of the heavy particle. In a weak-coupling limit (many interactions with few effect), we show that the solutions of jump process converge in law in the appropriate space towards the solution of a Lindbald master equation. To the best of our knowledge, it seems to be the first rigorous derivation of a dissipative quantum evolution equation.