Unconditional uniqueness for the cubic Gross-Pitaevskii hierarchy via quantum de Finetti

Abstract

We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in ${\mathbb{R}}^3$. One of the main tools in our analysis is the quantum de Finetti theorem. Our uniqueness result is equivalent to the one established in the celebrated works of Erdös, Schlein and Yau, \cite{esy1,esy2,esy3,esy4}.

AMS Latex, 34 pages. 2 figures

References in corpus (4)

• On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• The Mathematics of the Bose Gas and its Condensation
• Derivation of a Nonlinear Schrödinger Equation with a General power-type nonlinerity

Cited by in corpus (35)

• Ground states of large bosonic systems: The gross-pitaevskii limit revisited
• Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation
• Gross-Pitaevskii Dynamics for Bose-Einstein Condensates
• Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
• Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy
• Global Well-posedness of the NLS System for infinitely many fermions
• The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-body Evolution
• Mean-field limit of Bose systems: rigorous results
• The Derivation of the ${\mathbb{T}}^3$ Energy-critical NLS from Quantum Many-body Dynamics
• On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy
• Higher order corrections to the mean-field description of the dynamics of interacting bosons
• 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
• On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti
• The Gross-Pitaevskii hierarchy on general rectangular tori
• Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation
• The Cauchy problem and BEC stability for the quantum Boltzmann-Condensation system for bosons at very low temperature
• The rigorous derivation of the ${\mathbb{T}}^2$ focusing cubic NLS from 3D
• Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space
• The unconditional uniqueness for the energy-supercritical NLS
• Uniqueness of Solutions to the Spectral Hierarchy in Kinetic Wave Turbulence Theory
• A fermionic de Finetti theorem
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity
• The Unconditional Uniqueness for the Energy-critical Nonlinear Schrödinger Equation on ${\mathbb{T}}^4$
• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms
• On well-posedness and uniqueness for general hierarchy equations of Gross-Pitaevskii and Hartree type
• Well/Ill-posedness of the Boltzmann Equation with Soft Potential
• Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
• Uniqueness of solutions to the 3D quintic Gross-Pitaevskii Hierarchy
• An infinite sequence of conserved quantities for the cubic Gross-Pitaevskii hierarchy on $\mathbb{R}$
• On the mean-field and semiclassical limit from quantum $N$-body dynamics
• On the scattering problem for infinitely many fermions in dimensions $d\ge 3$ at positive temperature
• Mean field dynamics of a quantum tracer particle interacting with a boson gas
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate