The time-convolutionless quantum master equation is an exact description of the nonequilibrium dynamics of open quantum systems, with the advantage of being local in time. We derive a perturbative expansion to arbitrary order in the system-reservoir coupling for its generator, which contains significantly fewer terms than the ordered-cumulant expansion. We show that the derived expansion also admits a simple recursive formulation. The derived series is then used to describe the nonequilibrium dynamics of a quantum dot, including coherences. We find a relation between the generator and a generalization of the
T-matrix. Even though the
T-matrix rate equations are plagued by divergences, we show that these cancel order by order in the generator of the time-convolutionless master equation. This generalizes previous work on the time-convolutionless Pauli master equation, which does not include coherences, and lays the ground for possible numerical evaluations and analytical resummations.
The research was chiefly concerned with coherence effects in electromagnetic fields. Both free fields and fields interacting with matter were considered. Master equation techniques were applied to problems involving spontaneous emission. Fluctuation-dissipation theorems for systems in non-thermal equilibrium were derived and applied to the study of the laser threshold region. The exact mode expansion was derived for the electromagnetic field in a spatially dispersive model dielectric forming a plane parallel slab and was applied to the problem of refraction and reflection on a spatially dispersive half-space. A new derivation was obtained of the multipole expansion of an electromagnetic field generated by a localized monochromatic charge-current distribution. New representation for the multipole moments was also found.
We present a remarkably simple derivation of an exact time-local master equation describing the dynamics of quantum states in harmonic traps subject to arbitrary fluctuating forces. The relation between our master equation and known master equations of irreversible harmonic oscillator dynamics are established. Motivated by recent experiments, we focus on decoherence and in particular on the precise decoherence dynamics of a superposition of wave packets. We determine the decaying purity resulting from the time evolution based on our master equation and study its connection to experimentally accessible observables. Finally, we discuss the heating of the system subjected to arbitrary Gaussian noise.