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 (17)

• Proof of Bose-Einstein Condensation for Dilute Trapped Gases
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
• A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas
• On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Second-order corrections to mean field evolution for weakly interacting Bosons. I
• Rigorous Derivation of the Gross-Pitaevskii Equation with a Large Interaction Potential
• Bose-Einstein Quantum Phase Transition in an Optical Lattice Model
• Mean-Field- and Classical Limit of Many-Body Schrödinger Dynamics for Bosons
• On the Klainerman-Machedon Conjecture of the Quantum BBGKY Hierarchy with Self-interaction
• On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with A Quadratic Trap
• Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in $d=3$ based on spacetime norms
• Derivation of the time dependent Gross-Pitaevskii equation without positivity condition on the interaction
• On the uniqueness of solutions to the periodic 3D 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 (37)

• Ground states of large bosonic systems: The gross-pitaevskii limit revisited
• Gross-Pitaevskii Dynamics for Bose-Einstein Condensates
• Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation
• On the Klainerman-Machedon Conjecture of the Quantum BBGKY Hierarchy with Self-interaction
• On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
• Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
• Global Well-posedness of the NLS System for infinitely many fermions
• Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy
• 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
• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms
• 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 ${\mathbb{T}}^4$
• Uniqueness of solutions to the 3D quintic Gross-Pitaevskii Hierarchy
• Well/Ill-posedness of the Boltzmann Equation with Soft Potential
• Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
• On well-posedness and uniqueness for general hierarchy equations of Gross-Pitaevskii and Hartree type
• 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