Time Reversal Invariance of quantum kinetic equations II: Density operator formalism

摘要

Time reversal symmetry is a fundamental property of many quantum mechanicalsystems. The relation between statistical physics and time reversal is subtleand not all statistical theories conserve this particular symmetry, mostnotably hydrodynamic equations and kinetic equations such as the Boltzmannequation. Here we consider quantum kinetic generalizations of the Boltzmannequation by using the method of reduced density operators leading to thequantum generalization of the BBGKY-(Bogolyubov, Born, Green, Kirkwood, Yvon)hierachy. We demonstrate that all commonly used approximations, includingVlasov, Hartree-Fock and the non-Markovian generalizations of the Landau,T-matrix and Lenard-Balescu equations are originally time-reversal invariant,and we formulate a general criterion for time reversibility of approximationsto the quantum BBGKY-hierarchy. Finally, we illustrate, on the example of theBorn approximation, how irreversibility is introduced into quantum kinetictheory via the Markov limit, making the connection with the standard Boltzmannequation. This paper is a complement to paper I [Scharnke {\it et al.},submitted to J. Math. Phys., arXiv:1612.08033] where time-reversal invarianceof quantum-kinetic equations was analyzed in the frame of the independentnonequilibrium Green functions formalism.