Mean-Field Dynamics of Fermions with Relativistic Dispersion

Abstract

We extend the derivation of the time-dependent Hartree-Fock equation recently obtained in [2] to fermions with a relativistic dispersion law. The main new ingredient is the propagation of semiclassical commutator bounds along the pseudo-relativistic Hartree-Fock evolution.

11 pages

References in corpus (2)

• Classical limit for semi-relativistic Hartree systems
• Stellar Collapse in the Time Dependent Hartree-Fock Approximation

Cited by in corpus (24)

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• A New Method and a New Scaling For Deriving Fermionic Mean-field Dynamics
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• Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime
• Correlation Energy of a Weakly Interacting Fermi Gas
• The dilute Fermi gas via Bogoliubov theory
• Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential
• Hartree Corrections in a Mean-field Limit for Fermions with Coulomb Interaction
• Local existence of solutions to Randomized Gross-Pitaevskii hierarchies
• Combined mean-field and semiclassical limits of large fermionic systems
• Classical Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
• Mean-field Dynamics for the Nelson Model with Fermions
• Semi-classical limit of large fermionic systems at positive temperature
• From Hartree dynamics to the relativistic Vlasov equation
• Effective Dynamics of Extended Fermi Gases in the High-Density Regime
• Bosonic Collective Excitations in Fermi Gases
• 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
• Convergence towards the Vlasov-Poisson Equation from the $N$-Fermionic Schrödinger Equation
• An optimal semiclassical bound on certain commutators
• Dynamics of mean-field Fermi systems with nonzero pairing
• Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation
• Derivation of Vlasov equations for multi-species fermions