Secular master equation for adiabatically time dependent systems

TL;DR

This paper derives a Lindblad-form master equation for adiabatically time-dependent quantum systems, demonstrating the validity of the secular approximation in this context and showing environmental coupling can enhance adiabaticity.

Contribution

It presents a first-principles derivation of a master equation for slowly varying Hamiltonians, clarifying the secular approximation's applicability and applying it to the Landau-Zener problem.

Findings

Secular approximation valid for slow time-dependent Hamiltonians in an appropriate basis.

Coupling to a low-temperature environment improves adiabaticity.

Derived a general Lindblad master equation for adiabatic systems.

Abstract

Relying only on first principles, we derive a master equation of Lindblad form generally applicable for adiabatically time dependent systems. Our analysis shows that the much debated secular approximation can be valid for slowly time dependent Hamiltonians when performed in an appropriate basis. We apply our approach to the well known Landau-Zener problem where we find that adiabaticity is improved by coupling to a low temperature environment.