“Global” and “Local” Approaches to the Theory of Open Quantum Optical Systems

Abstract

The application of “exact/complete” initial Hamiltonian of an open optical system and its surroundings and “approximate” effective Hamiltonian for the derivation of the kinetic equation of the open optical system is analyzed in the conditions of the Markovian approximation and the representation of the open system surroundings (thermostat) as a delta-correlated noise. It is shown that the characteristic time hierarchy of the open system naturally necessitates a transition from the aforementioned exact Hamiltonian to the approximate effective Hamiltonian for the subsequent use of the Markovian approximation and the model of delta-correlated surroundings of the open system in the local approach. The Schrodinger equation for the wavevector of the open system and its surroundings is a quantum stochastic differential equation, from which the kinetic equation describing both familiar and new results can be derived easily in the standard manner.