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A Quantum Kinetic Master Equation (QKME) for bosonic atoms is formulated. Itis a quantum stochastic equation for the kinetics of a dilute quantum Bose gas,and describes the behavior and formation of Bose condensation. The keyassumption in deriving the QKME is a Markov approximation for the atomiccollision terms. In the present paper the basic structure of the theory isdeveloped, and approximations are stated and justified to delineate the regionof validity of the theory. Limiting cases of the QKME include the QuantumBoltzmann master equation and the Uehling-Uhlenbeck equation, as well as anequation analogous to the Gross-Pitaevskii equation.Comment: 37 pages, 4 figure

Quantum kinetic theory: A quantum kinetic master equation for condensation of a weakly interacting Bose gas without a trapping potential