Propagation of Moments for Large Data and Semiclassical Limit to the Relativistic Vlasov Equation

Abstract

We investigate the semiclassical limit from the semirelativistic Hartree–Fock equation describing the time evolution of a system of fermions in the mean-field regime with a relativistic dispersion law and interacting through a singular potential of the form , , , and , with the convention if . For mixed states, we show convergence in the Schatten norms with an explicit rate towards the Weyl transform of a solution to the relativistic Vlasov equation with singular potentials, thus generalizing [E. Dietler, S. Rademacher, and B. Schlein, J. Stat. Phys., 172 (2018), pp. 398–433], where the case of smooth potentials has been treated. Moreover, we provide new results on the well-posedness theory of the relativistic Vlasov equations with singular interactions.