From Hartree dynamics to the relativistic Vlasov equation

Abstract

We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the non-relativistic setting have been recently obtained in [6]. The new challenge that we have to face here, in the relativistic setting, consists in controlling the difference between the quantum kinetic energy and the relativistic transport term appearing in the Vlasov equation.

30 pages

References in corpus (4)

• From the Hartree dynamics to the Vlasov equation
• Mean-Field Dynamics of Fermions with Relativistic Dispersion
• A New Method and a New Scaling For Deriving Fermionic Mean-field Dynamics
• Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction

Cited by in corpus (6)

• Combined mean-field and semiclassical limits of large fermionic systems
• Semi-classical limit of large fermionic systems at positive temperature
• A mixed-norm estimate of the two-particle reduced density matrix of many-body Schrödinger dynamics for deriving the Vlasov equation
• Propagation of moments for large data and semiclassical limit to the relativistic Vlasov equation
• Convergence towards the Vlasov-Poisson Equation from the $N$-Fermionic Schrödinger Equation
• Derivation of Vlasov equations for multi-species fermions