Global well-posedness of the NLS system for infinitely many fermions

DOI10.1007/s00205-016-1068-xzbMath1369.35075arXiv1512.04674OpenAlexW3102283705MaRDI QIDQ522181

Thomas Chen, Younghun Hong, Nataša Pavlović

Publication date: 13 April 2017

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.04674

zbMATH Keywords

density matrixPauli principleStrichartz estimatesHartree equations

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) PDEs in connection with quantum mechanics (35Q40)

Related Items (21)

Strichartz estimates for \(N\)-body Schrödinger operators with small potential interactions ⋮ Stability of steady states for Hartree and Schrödinger equations for infinitely many particles ⋮ On the well-posedness and stability of cubic and quintic nonlinear Schrödinger systems on \(\mathbb{T}^3\) ⋮ On the scattering problem for infinitely many fermions in dimensions \(d\geq 3\) at positive temperature ⋮ Strong solutions for the Alber equation and stability of unidirectional wave spectra ⋮ On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate ⋮ Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations ⋮ Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates ⋮ Global existence versus finite time blowup dichotomy for the system of nonlinear Schrödinger equations ⋮ Stability of equilibria for a Hartree equation for random fields ⋮ About systems of fermions with large number of particles: a probabilistic point of view ⋮ The nonlinear Schrödinger equation for orthonormal functions: existence of ground states ⋮ Long-time behaviour of time-dependent density functional theory ⋮ Counterexamples to \(L^p\) collapsing estimates ⋮ The Hartree equation with a constant magnetic field: well-posedness theory ⋮ The orthonormal Strichartz inequality on torus ⋮ A diffusion result for the Hartree equation around non-localised solutions ⋮ Uniform in N estimates for a Bosonic system of Hartree–Fock–Bogoliubov type ⋮ On the Strichartz estimates for orthonormal systems of initial data with regularity ⋮ Maximal estimates for the Schrödinger equation with orthonormal initial data ⋮ The Hartree and Vlasov equations at positive density

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Strichartz inequality for orthonormal functions
• The Hartree equation for infinitely many particles. II: Dispersion and scattering in 2D
• The mathematics of the Bose gas and its condensation.
• The quintic NLS as the mean field limit of a boson gas with three-body interactions
• A microscopic derivation of the time-dependent Hartree-Fock equation with Coulomb two-body interaction
• Derivation of the cubic nonlinear Schrödinger equation from quantum dynamics of many-body systems
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
• 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
• Mean field dynamics of fermions and the time-dependent Hartree-Fock equation
• Derivation of the Schrödinger-Poisson equation from the quantum \(N\)-body problem
• Nonlinear Hartree equation as the mean field limit of weakly coupled fermions
• A positive density analogue of the Lieb-Thirring inequality
• On the generalized semi-relativistic Schrödinger-Poisson system in \(\mathbb{R}^n\)
• The Hartree equation for infinitely many particles. I: Well-posedness theory
• Derivation of a nonlinear Schrödinger equation with a general power-type nonlinearity in \(d=1,2\).
• Mean-field- and classical limit of many-body Schrödinger dynamics for bosons
• Derivation of Hartree's theory for generic mean-field Bose systems
• Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in \(d=3\) based on spacetime norms
• Higher Order Energy Conservation and Global Well-Posedness of Solutions for Gross-Pitaevskii Hierarchies
• Unconditional Uniqueness for the Cubic Gross-Pitaevskii Hierarchy via Quantum de Finetti
• Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
• On the Vlasov hierarchy
• The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation
• Endpoint Strichartz estimates
• Space‐time estimates for null forms and the local existence theorem
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Correlation Structures, Many-Body Scattering Processes, and the Derivation of the Gross–Pitaevskii Hierarchy
• Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates
• Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
• Mean-field evolution of fermionic systems

This page was built for publication: Global well-posedness of the NLS system for infinitely many fermions