A new proof of existence of solutions for focusing and defocusing Gross-Pitaevskii hierarchies
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Publication:4911564
DOI10.1090/S0002-9939-2012-11308-5zbMath1260.35197arXiv0906.3277OpenAlexW2007638502MaRDI QIDQ4911564
Publication date: 19 March 2013
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0906.3277
NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01)
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Cites Work
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- 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
- Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies
- 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
- On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
- On the Cauchy problem for focusing and defocusing Gross-Pitaevskii hierarchies
- 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
- Rigorous derivation of the cubic NLS in dimension one
- On long range behaviour of van der Waals force
- 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
- Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice
- On the Cauchy problem for Gross–Pitaevskii hierarchies
- A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas
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