Microscopic theory of energy dissipation and decoherence in solid-state systems: A reformulation of the conventional Markov limit

TL;DR

This paper introduces a new density-matrix approach for modeling energy dissipation and decoherence in open quantum systems that overcomes limitations of the traditional Markov approximation, ensuring positivity and accurate semiclassical behavior.

Contribution

The authors propose an alternative adiabatic scheme with temporal symmetrization and coarse graining that yields a Lindblad-like dynamics without positivity issues, improving upon the conventional Markov limit.

Findings

The new formalism maintains positivity at all times.

It accurately reproduces Fermi's golden rule in the semiclassical limit.

Application to semiconductor quantum dots shows improved modeling of phonon interactions.

Abstract

We present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the proposed alternative adiabatic scheme does not threaten positivity at any time. The key idea of our approach rests in the temporal symmetrization and coarse graining of the scattering term in the Liouville-von Neumann equation, before applying the reduction procedure over the environment degrees of freedom. The resulting dynamics is genuinely Lindblad-like and recovers the Fermi's golden rule features in the semiclassical limit. Applications to the prototypical case of a semiconductor quantum dot exposed to incoherent phonon excitation peaked around a central mode are discussed, highlighting the success of our formalism with respect to the critical issues of the conventional Markov limit.