A generalized master equation for time-dependent Hamiltonians

D. N. Zubarev, В. П. Калашников

I. Kamleitner

Relying only on first principles, we derive a master equation of Lindblad form generally applicable for adiabatically driven 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.

Ladislav Šamaj

Francisco Soto, Braulio Misael Villegas-Martínez, H. M. Moya-Cessa

Boris Leaf

For a system described in a phase space of generalized coordinates w and momenta J, the generalized master equation gives the time evolution of the reduced-density distribution function ρ(t, J) for the momenta. A generalization of the generalized master equation, having a similar non-Markoffian form, is derived for the full distribution function ρ(t, w, J). This equation is an alternate form of the Liouville equation. The derivation is an extension of a previous derivation of the generalized master equation from the Liouville equation utilizing projection operators in a Hilbert space. The time-evolution equation for the reduced distribution function ρr(t, wr, J), depending on the subset wr of the set of coordinates w, is derived. The approach to a stationary state for t → ∞ is discussed.

Dimitri R. Yafaev