Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data
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Publication:2235189
DOI10.1016/j.anihpc.2021.01.004zbMath1484.82024arXiv1902.08520OpenAlexW2917473395MaRDI QIDQ2235189
Publication date: 20 October 2021
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1902.08520
nonlinear Schrödinger equationsemiclassical limitVlasov equationCoulomb interactiongravitational interactionHartree equation
NLS equations (nonlinear Schrödinger equations) (35Q55) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Vlasov equations (35Q83) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Related Items (6)
Effective dynamics of interacting fermions from semiclassical theory to the random phase approximation ⋮ Global-in-time semiclassical regularity for the Hartree–Fock equation ⋮ Propagation of Moments for Large Data and Semiclassical Limit to the Relativistic Vlasov Equation ⋮ Strong semiclassical limits from Hartree and Hartree-Fock to Vlasov-Poisson equations ⋮ The Magnetic Liouville Equation as a Semiclassical Limit ⋮ On the \(L^2\) rate of convergence in the limit from the Hartree to the Vlasov-Poisson equation
Cites Work
- Unnamed Item
- Unnamed Item
- On the mean field and classical limits of quantum mechanics
- From the Hartree dynamics to the Vlasov equation
- The Schrödinger equation in the mean-field and semiclassical regime
- A microscopic derivation of the time-dependent Hartree-Fock equation with Coulomb two-body interaction
- A simple derivation of mean field limits for quantum systems
- Strong semiclassical approximation of Wigner functions for the Hartree dynamics
- On the mean-field limit of bosons with Coulomb two-body interaction
- Uniqueness of the solution to the Vlasov--Poisson system with bounded density
- Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction
- On an inequality of Lieb and Thirring
- Quantum fluctuations and rate of convergence towards mean field dynamics
- The global Cauchy problem for the nonlinear Schrödinger equation revisited
- Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data
- 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
- On a class of non linear Schrödinger equations with non local interactions
- Propagation of space moments in the Vlasov-Poisson equation and further results
- On Wigner measures
- Derivation of the Schrödinger-Poisson equation from the quantum \(N\)-body problem
- Weak coupling limit of the \(N\)-particle Schrödinger equation
- On the derivation of the Hartree equation from the \(N\)-body Schrödinger equation: uniformity in the Planck constant
- A new method and a new scaling for deriving fermionic mean-field dynamics
- Wave packets and the quadratic Monge-Kantorovich distance in quantum mechanics
- Smoothing effect for some Schrödinger equations
- Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
- Empirical measures and quantum mechanics: applications to the mean-field limit
- Propagation of moments and semiclassical limit from Hartree to Vlasov equation
- Mean field evolution of fermions with Coulomb interaction
- Mean-field evolution of fermions with singular interaction
- 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
- Mean-Field Evolution of Fermionic Mixed States
- Space Moments of the Vlasov--Poisson System: Propagation and Regularity
- MEAN-FIELD APPROXIMATION OF QUANTUM SYSTEMS AND CLASSICAL LIMIT
- The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation
- Global existence of smooth solutions to the vlasov poisson system in three dimensions
- Semiclassical, $t\rightarrow \infty $ asymptotics and dispersive effects for Hartree-Fock systems
- Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner–Poisson and Schrödinger‐Poisson systems
- Homogenization limits and Wigner transforms
- L2 Solutions to the Schrödinger–Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects
- THE CLASSICAL LIMIT OF A SELF-CONSISTENT QUANTUM-VLASOV EQUATION IN 3D
- TIME-DEPENDENT RESCALINGS AND LYAPUNOV FUNCTIONALS FOR THE VLASOV–POISSON AND EULER–POISSON SYSTEMS, AND FOR RELATED MODELS OF KINETIC EQUATIONS, FLUID DYNAMICS AND QUANTUM PHYSICS
- Passage from Quantum to Classical Molecular Dynamics in the Presence of Coulomb Interactions
- Hartree corrections in a mean-field limit for fermions with Coulomb interaction
- Semiclassical limit of quantum dynamics with rough potentials and well‐posedness of transport equations with measure initial data
- Moment Propagation for Weak Solutions to the Vlasov–Poisson System
- Bogoliubov corrections and trace norm convergence for the Hartree dynamics
- Mean-field evolution of fermionic systems
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