Derivation in Strong Topology and Global Well-Posedness of Solutions to the Gross-Pitaevskii Hierarchy

DOI10.1080/03605302.2014.917380zbMath1301.35147arXiv1305.1404OpenAlexW2962946181MaRDI QIDQ2926038

Kenneth Taliaferro, Thomas Chen

Publication date: 29 October 2014

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.1404

zbMATH Keywords

BBGKY hierarchyglobal well-posednessGross-Pitaevskii hierarchyderivation of NLSinfinite rank limitquantum de Finetti

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Many-body theory; quantum Hall effect (81V70)

Related Items (15)

The Gross-Pitaevskii hierarchy on general rectangular tori ⋮ Quantitative derivation and scattering of the 3D cubic NLS in the energy space ⋮ Uniqueness of solutions to the spectral hierarchy in kinetic wave turbulence theory ⋮ Unconditional Uniqueness of the cubic Gross--Pitaevskii Hierarchy with Low Regularity ⋮ Unconditional Uniqueness for the Cubic Gross-Pitaevskii Hierarchy via Quantum de Finetti ⋮ Uniqueness of solutions to the 3D quintic Gross-Pitaevskii hierarchy ⋮ On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti ⋮ On well-posedness for general hierarchy equations of Gross-Pitaevskii and Hartree type ⋮ On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate ⋮ Negative energy blowup results for the focusing Hartree hierarchy via identities of virial and localized virial type ⋮ The rigorous derivation of the \(\mathbb{T}^2\) focusing cubic NLS from 3D ⋮ Randomization and the Gross-Pitaevskii hierarchy ⋮ Focusing quantum many-body dynamics. II: The rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation from 3D ⋮ Unconditional uniqueness for the energy-critical nonlinear Schrödinger equation on ⋮ Derivation of the quintic NLS from many-body quantum dynamics in \(\mathbb T^2\)

Cites Work

• Unnamed Item
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• Unnamed Item
• Pair excitations and the mean field approximation of interacting Bosons. I
• Collapsing estimates and the rigorous derivation of the 2d cubic nonlinear Schrödinger equation with anisotropic switchable quadratic traps
• Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
• The mathematics of the Bose gas and its condensation.
• Second-order corrections to mean field evolution of weakly interacting bosons. I
• The quintic NLS as the mean field limit of a boson gas with three-body interactions
• Second-order corrections to mean field evolution of weakly interacting bosons. II
• Rate of convergence towards Hartree dynamics
• A simple derivation of mean field limits for quantum systems
• Rate of convergence towards the Hartree-von Neumann limit in the mean-field regime
• Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies
• Second-order corrections to mean field evolution for weakly interacting bosons in the case of three-body interactions
• Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons
• On the mean-field limit of bosons with Coulomb two-body interaction
• Derivation of the cubic nonlinear Schrödinger equation from quantum dynamics of many-body systems
• The Cauchy problem for the nonlinear Schrödinger equation in \(H^ 1\)
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• On the Cauchy problem for focusing and defocusing Gross-Pitaevskii hierarchies
• Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
• Mean field limit for bosons and infinite dimensional phase-space analysis
• Quantum fluctuations and rate of convergence towards mean field dynamics
• Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
• Mean-field- and classical limit of many-body Schrödinger dynamics for bosons
• On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamics
• Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in \(d=3\) based on spacetime norms
• On the rigorous derivation of the 3D cubic nonlinear Schrödinger equation with a quadratic trap
• Symmetric states of infinite tensor products of \(C^ *\)-algebras
• Rigorous derivation of the cubic NLS in dimension one
• Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential
• Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
• Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate
• Atomism and quantization
• A PRIORI ESTIMATES FOR MANY-BODY HAMILTONIAN EVOLUTION OF INTERACTING BOSON SYSTEM
• Locally normal symmetric states and an analogue of de Finetti's theorem
• A new proof of existence of solutions for focusing and defocusing Gross-Pitaevskii hierarchies
• Multilinear Morawetz identities for the Gross-Pitaevskii hierarchy
• A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas

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