From Markovian semigroup to non-Markovian quantum evolution

TL;DR

This paper introduces a new class of memory kernels for quantum evolution that ensure physical validity and includes a normalization method, connecting non-Markovian and Markovian dynamics.

Contribution

It presents a novel construction of memory kernels for quantum dynamics that guarantees complete positivity and trace preservation, bridging non-Markovian and Markovian regimes.

Findings

New class of legitimate memory kernels for quantum evolution

Normalization procedure ensures physical validity of dynamics

Recovers standard Markovian evolution in Wigner-Weisskopf theory

Abstract

We provided a class of legitimate memory kernels leading to completely positive trace preserving dynamical maps. Our construction is based on a simple normalization procedure. Interestingly, when applied to the celebrated Wigner-Weisskopf theory it gives the standard Markovian evolution governed by the local master equation.