Quantum Vlasov equation and its Markov limit - art. no. 125015

The adiabatic particle number in mean field theory obeys a quantum Vlasov e quation which is nonlocal in time. For weak, slowly varying electric fields this particle number can be identified with the single particle distributi on function in phase space, and its time rate of change is the appropriate effective source term for the Boltzmann-Vlasov equation. By analyzing the e volution of the particle number we exhibit the time structure of the partic le creation process in a constant electric field, and derive the local form of the source term due to pair creation. In order to capture the secular S chwinger creation rare, the source term requires an asymptotic expansion wh ich is uniform in time, and whose longitudinal momentum dependence can be a pproximated by a delta function only on time scales much longer than root p (perpendicular to)(2)+m(2)c(2)/eE. The local Vlasov source term amounts to a kind of Markov limit of field theory, where information about quantum pha se correlations: in the created pairs is ignored and a reversible Hamiltoni an evolution is replaced by an irreversible kinetic one. This replacement h as a precise counterpart in the density matrix description, where it corres ponds to disregarding the rapidly varying off-diagonal terms in the adiabat ic number basis and treating the more slowly varying diagonal elements as t he probabilities of creating pairs in a stochastic process. A numerical com parison between the quantum and local kinetic approaches to the dynamical b ack reaction problem shows remarkably good agreement, even in quite strong electric fields. eE similar or equal to m(2)c(3)/(h) over bar, over a large range of times. [S0556-2821(98)04520-2].