Starting from a total Hamiltonian, the second order weak coupling approximation to arrive to a Quantum Master Equation for a system interacting with a thermal bath, is revisited. Then a Kossakowski-Lindblad form for the generator is written in terms of the position and momentum operators. Some conditions on the coefficients of this generator are analyzed in order to fulfill a well behaved evolution. A weak coupling approximation for an stochastic non-Markovian wave equation is also worked out.
As an example, we analyze a free particle interacting with a thermal quantum environment. In the context of Schrödinger-Langevin picture different kinds of interactions with the bath are analyzed. Introducing this stochastic state we give a phenomenological point of view in order to overcome certain difficulties in the master equation of the system --in the second order approximation--and also to represent the open free particle state dynamics.
TRABAJO PRESENTADO COMO POSTER POR AK CHATTAH
