In this work an alternative way to obtaning the Kossakowski-Lindblad semigroup, which allows to study the dynamic evolution of open quantum systems is presented.
We start from the Schröedinger-Langevin picture for the wave function of the quantum system. The noise present in this equation is a non-white one, and contains all the information about the temperature and the quantum structure ot the thermal bath. In this work, the correlation funtion of the noise comes from considering the thermal bath as represented by an infinite set of harmonic oscillators. From this picture we study the evolution of the average of the density matrix; this is done by making a cumulant expansion in the small Kubo number. Doing this, we obtain an Quantum Master Equation (QME), that preserves the norm of the density matrix at all time. This QME can be applied to every kind of system, all we have to know is the set of operators, which represents the interaction between the system and the thermal bath.
This approach is applied to the free particle Hamiltonian in the continous and discrete regimes. We first analize the discrete case obtaining the evolution equation for the position operator which shows a diffusive behavior. In the continous case, different models for the interaction operators are analized, given in each case the evolution equations for the position and momentum operators. In each case the diffusive and non diffusive results are analized. In the classical limit, the Fokker-Planck equation is obtaned.
POSTER PRESENTADO POR A.K. CHATTAH
