Positivity violation and initial slips in open systems

Abstract

Master equations without Lindblad form can in principle violate the positivity of the density operator. However, when such a master equation arises through systematic adiabatic elimination of fast variables from underlying microscopic dynamics, the violation can at worst arise on time scales one has coarsegrained over when performing the adiabatic elimination and can thus simply be ignored. Examples of non-Lindblad master equations are shown to arise for the Ornstein Uhlenbeck process both at high and low temperatures and for a single-mode laser operated near threshold.