Semi-classical limit of quantum free energy minimizers for the gravitational Hartree equation
DOI10.1007/s00205-020-01585-5zbMath1456.81188arXiv1909.13192OpenAlexW2976177463MaRDI QIDQ2220644
Woocheol Choi, Jinmyoung Seok, Younghun Hong
Publication date: 25 January 2021
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1909.13192
stabilitygravitational fieldsstellar dynamicsclassical limitVlasov equationHartree-Fock approximationmany body systemsquantum limitfree energy minimizers
Quantum field theory on curved space or space-time backgrounds (81T20) Methods of quantum field theory in general relativity and gravitational theory (83C47) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Galactic and stellar structure (85A15) Celestial mechanics (70F15) Galactic and stellar dynamics (85A05) Statistical thermodynamics (82B30)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the mean field and classical limits of quantum mechanics
- From the Hartree dynamics to the Vlasov equation
- Strichartz inequality for orthonormal functions
- Thermal effects in gravitational Hartree systems
- Orbital stability of spherical galactic models
- Spectral density and Sobolev inequalities for pure and mixed states
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- Uniqueness of ground states for pseudorelativistic Hartree equations
- Orbital stability for polytropic galaxies
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- The orbital stability of the ground states and the singularity formation for the gravitational Vlasov-Poisson system
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- Conservation laws and time decay for the solutions of some nonlinear Schrödinger-Hartree equations and systems
- Propagation of moments and regularity for the 3-dimensional Vlasov- Poisson system
- Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
- An existence proof for the Hartree-Fock time-dependent problem with bounded two-body interaction
- The time-dependent Hartree-Fock equations with Coulomb two-body interaction
- On nonlinear stability of polytropic galaxies
- Stable steady states in stellar dynamics
- On Wigner measures
- Existence and nonlinear stability of stationary states of the Schrödinger-Poisson system
- Uniqueness and symmetry of ground states for higher-order equations
- Asymptotic behaviour for the Vlasov-Poisson system in the stellar-dynamics case
- Steady states in galactic dynamics
- Variational method for stable polytropic galaxies
- On the Strichartz estimates for orthonormal systems of initial data with regularity
- The classical limit of the Heisenberg and time-dependent Hartree-Fock equations: the Wick symbol of the solution
- The semiclassical limit of the time dependent Hartree-Fock equation: the Weyl symbol of the solution
- Cwikel's theorem and the CLR inequality
- A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
- Mean-Field Evolution of Fermionic Mixed States
- ORBITALLY STABLE STATES IN GENERALIZED HARTREE–FOCK THEORY
- Global existence of smooth solutions to the vlasov poisson system in three dimensions
- On the asymptotic growth of the solutions of the vlasov-poisson system
- L2 Solutions to the Schrödinger–Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects
- Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates
- A new variational approach to the stability of gravitational systems
- Isotropic steady states in galactic dynamics
