Improved stability for 2D attractive Bose gases

DOI10.1063/1.5131320zbMath1439.81099arXiv1909.08902OpenAlexW3008706699MaRDI QIDQ5110735

Nicolas Rougerie, Phan Thành Nam

Publication date: 22 May 2020

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.08902

zbMATH Keywords

magnetic fieldsBose gaszero point energyprobability theoryself-adjoint operatorsoperator theoryquantum measurement theorybosonsinteratomic potentialsdensity-matrix

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Quantum measurement theory, state operations, state preparations (81P15) Statistical mechanics of gases (82D05) Quantum state spaces, operational and probabilistic concepts (81P16) Bosonic systems in quantum theory (81V73)

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Cites Work

• Unnamed Item
• Ground states of large bosonic systems: the Gross-Pitaevskii limit revisited
• The mathematics of the Bose gas and its condensation.
• Nonlinear Schrödinger equations and sharp interpolation estimates
• The ground state energy of dilute Bose gas in potentials with positive scattering length
• Ground state energy of dilute Bose gas in small negative potential case
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
• Derivation of the time dependent two dimensional focusing NLS equation
• Derivation of the time dependent Gross-Pitaevskii equation in two dimensions
• Quantum de Finetti theorems under local measurements with applications
• Norm approximation for many-body quantum dynamics: Focusing case in low dimensions
• On the mass concentration for Bose-Einstein condensates with attractive interactions
• The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases
• Effective Evolution Equations from Quantum Dynamics
• A note on 2D focusing many-boson systems
• On the Symmetry of the Ground States of Nonlinear Schrödinger Equation with Potential
• Derivation of the Dipolar Gross--Pitaevskii Energy
• The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-Body Evolution
• A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas