Combined mean-field and semiclassical limits of large fermionic systems

Abstract

We study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale $\hslash =N^{-1/3}$ in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for the k particle Husimi measure. Further estimates are derived to obtain the weak compactness of the Husimi measure, and in addition uniform estimates for the remainder terms in the hierarchy are derived in order to show that in the semiclassical regime the weak limit of the Husimi measure is exactly the solution of the Vlasov equation.

arXiv commentArticle has been peer-reviewed and published. We update the oscillation estimate parts

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Cited by in corpus (6)

• From many-body quantum dynamics to the Hartree-Fock and Vlasov equations with singular potentials
• On the $L^2$ Rate of Convergence in the Limit from the Hartree to the Vlasov$\unicode{x2013}$Poisson Equation
• Bosonization of Fermionic Many-Body Dynamics
• 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