Convergence towards the Vlasov-Poisson Equation from the $N$-Fermionic Schrödinger Equation

Abstract

We consider the quantum dynamics of $N$ interacting fermions in the large $N$ limit. The particles in the system interact with each other via repulsive interaction that is regularized Coulomb potential with a polynomial cutoff with respect to $N$.From the quantum system, we derive the Vlasov-Poisson system by simultaneously estimating the semiclassical and mean-field residues in terms of the Husimi measure.

References in corpus (19)

• Negativity of the Wigner function as an indicator of nonclassicality
• On the Mean Field and Classical Limits of Quantum Mechanics
• Classical to Quantum Transition of a Driven Nonlinear Nanomechanical Resonator
• Rate of Convergence Towards Hartree Dynamics
• Mean-field Evolution of Fermionic Systems
• The Schrödinger Equation in the Mean-Field and Semiclassical Regime
• Extending Hudson's theorem to mixed quantum states
• Mean field evolution of fermions with Coulomb interaction
• 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
• The classical limit of the time dependent Hartree-Fock equation. I. The Weyl symbol of the solution
• Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation
• Hartree Corrections in a Mean-field Limit for Fermions with Coulomb Interaction
• Semiclassical limit to the Vlasov equation with inverse power law potentials
• Combined mean-field and semiclassical limits of large fermionic systems
• From Hartree dynamics to the relativistic Vlasov equation
• Rate of Convergence towards Hartree Dynamics with Singular Interaction Potential

Cited by in corpus (1)

• Derivation of Vlasov equations for multi-species fermions