Quantum fluctuations and rate of convergence towards mean field dynamics

From MaRDI portal

Publication:1048088

Jump to:navigation, search

DOI10.1007/s00220-009-0867-4zbMath1186.82051arXiv0711.3087OpenAlexW2138377210MaRDI QIDQ1048088

Igor Rodnianski, Benjamin Schlein

Publication date: 11 January 2010

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

Full work available at URL: https://arxiv.org/abs/0711.3087

zbMATH Keywords

BBGKY hierarchy mean field dynamics Hartree equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10)

Related Items

Dependent random variables in quantum dynamics, Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field, Norm approximation for the Fröhlich dynamics in the mean-field regime, On the characterisation of fragmented Bose–Einstein condensation and its emergent effective evolution, Bogoliubov dynamics and higher-order corrections for the regularized Nelson model, Weak Edgeworth expansion for the mean-field Bose gas, Derivation of the Hartree equation for compound Bose gases in the mean field limit, Derivation of the Maxwell--Schrödinger Equations from the Pauli--Fierz Hamiltonian, Derivation of the 1d nonlinear Schrödinger equation from the 3d quantum many-body dynamics of strongly confined bosons, Mean-field evolution of fermionic systems, On some rigorous aspects of fragmented condensation, Classical limit of the Nelson model with cutoff, The quantumN-body problem in the mean-field and semiclassical regime, Rate of convergence toward Hartree type equations for mixture condensates with factorized initial data, Bogoliubov Spectrum of Interacting Bose Gases, Product-state approximations to quantum states, Bogoliubov corrections and trace norm convergence for the Hartree dynamics, Mean-field dynamics for mixture condensates via Fock space methods, Uniform in N estimates for a Bosonic system of Hartree–Fock–Bogoliubov type, Derivation of the time dependent Gross–Pitaevskii equation with external fields, Quantitative Derivation of the Gross‐Pitaevskii Equation, Rate of convergence in nonlinear Hartree dynamics with factorized initial data, The Gross-Pitaevskii hierarchy on general rectangular tori, On the mean field and classical limits of quantum mechanics, Focusing quantum many-body dynamics: the rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation, On the Klainerman-Machedon conjecture for the quantum BBGKY hierarchy with self-interaction, Mean field derivation of DNLS from the Bose-Hubbard model, Mean field dynamics of a quantum tracer particle interacting with a boson gas, The mean-field limit of the Lieb-Liniger model, A central limit theorem in many-body quantum dynamics, On the mean-field limit of bosons with Coulomb two-body interaction, Rate of Convergence to Mean Field for Interacting Bosons, On the derivation of the Hartree equation from the \(N\)-body Schrödinger equation: uniformity in the Planck constant, From bosonic grand-canonical ensembles to nonlinear Gibbs measures, The semi-classical limit of large fermionic systems, Poisson commuting energies for a system of infinitely many bosons, Mean field limit for bosons with compact kernels interactions by Wigner measures transportation, Derivation in Strong Topology and Global Well-Posedness of Solutions to the Gross-Pitaevskii Hierarchy, A new method and a new scaling for deriving fermionic mean-field dynamics, Derivation of the Landau-Pekar equations in a many-body mean-field limit, Pair excitations and the mean field approximation of interacting Bosons. I, Beyond Bogoliubov dynamics, Large deviation estimates for weakly interacting bosons, Unconditional Uniqueness of the cubic Gross--Pitaevskii Hierarchy with Low Regularity, Unconditional Uniqueness for the Cubic Gross-Pitaevskii Hierarchy via Quantum de Finetti, Gross-Pitaevskii dynamics for Bose-Einstein condensates, Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions \({d \leqslant 3}\), A simple proof of convergence to the Hartree dynamics in Sobolev trace norms, Uniqueness of solutions to the 3D quintic Gross-Pitaevskii hierarchy, Normalized standing waves for the Hartree equations, On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti, A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on \(\mathbb{T}^3\) from the dynamics of many-body quantum systems, On well-posedness for general hierarchy equations of Gross-Pitaevskii and Hartree type, Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction, 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, Dynamical collapse of Boson stars, Rate of convergence towards semi-relativistic Hartree dynamics, Wave packets and the quadratic Monge-Kantorovich distance in quantum mechanics, On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamics, Second-order corrections to mean field evolution of weakly interacting bosons. II, On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate, Rate of convergence towards Hartree dynamics, Derivation of Hartree's theory for generic mean-field Bose systems, Pair excitations and the mean field approximation of interacting Bosons, II, Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in \(d=3\) based on spacetime norms, A simple derivation of mean field limits for quantum systems, Rate of convergence towards the Hartree-von Neumann limit in the mean-field regime, Non linear Schrödinger limit of bosonic ground states, again, Derivation of the 1d Gross-Pitaevskii equation from the 3d quantum many-body dynamics of strongly confined bosons, Combined mean-field and semiclassical limits of large fermionic systems, Beyond mean field: on the role of pair excitations in the evolution of condensates, The rigorous derivation of the \(\mathbb{T}^2\) focusing cubic NLS from 3D, An infinite sequence of conserved quantities for the cubic Gross–Pitaevskii hierarchy on ℝ, Rate of convergence toward Hartree dynamics with singular interaction potential, Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data, Randomization and the Gross-Pitaevskii hierarchy, Higher order corrections to the mean-field description of the dynamics of interacting bosons, Derivation of 3D energy-critical nonlinear Schrödinger equation and Bogoliubov excitations for Bose gases, The Dirac-Frenkel principle for reduced density matrices, and the Bogoliubov-de Gennes equations, Quantum many-body fluctuations around nonlinear Schrödinger dynamics, Derivation of the time dependent two dimensional focusing NLS equation, A new proof of existence of solutions for focusing and defocusing Gross-Pitaevskii hierarchies, On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy, The Hartree equation for infinitely many particles. I: Well-posedness theory, Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states, Derivation of the time dependent Gross-Pitaevskii equation in two dimensions, Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies, Effective dynamics of a tracer particle interacting with an ideal Bose gas, Multivariate central limit theorem in quantum dynamics, Second-order corrections to mean field evolution for weakly interacting bosons in the case of three-body interactions, Mean-field dynamics for the Nelson model with fermions, Mean-field dynamics: Singular potentials and rate of convergence, Local existence of solutions to randomized Gross-Pitaevskii hierarchies, The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases, Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential, Uniform in \(N\) global well-posedness of the time-dependent Hartree-Fock-Bogoliubov equations in \(\mathbb {R}^{1+1}\), Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger, The NLS limit for Bosons in a quantum waveguide, Emergence of Time-Dependent Point Interactions in Polaron Models, Derivation of the Bogoliubov time evolution for a large volume mean-field limit, A large deviation principle in many-body quantum dynamics, Symmetric properties for Choquard equations involving fully nonlinear nonlocal operators, Quantum dynamics with mean field interactions: a new approach, Empirical measures and quantum mechanics: applications to the mean-field limit, On the time dependence of the rate of convergence towards Hartree dynamics for interacting bosons, The derivation of the \(\mathbb{T}^{3}\) energy-critical NLS from quantum many-body dynamics, Fluctuations of \(N\)-particle quantum dynamics around the nonlinear Schrödinger equation, Evolution of the Boson gas at zero temperature: Mean-field limit and second-order correction, Dynamics of large boson systems with attractive interaction and a derivation of the cubic focusing NLS equation in R3, Mean-Field Evolution of Fermionic Mixed States, Tracer particles coupled to an interacting boson gas, Propagation of moments and semiclassical limit from Hartree to Vlasov equation, Global estimates for the Hartree–Fock–Bogoliubov equations, Mean-field quantum dynamics with magnetic fields, On Bose-Einstein condensates in the Thomas-Fermi regime, Convergence rate towards the fractional Hartree equation with singular potentials in higher Sobolev trace norms, Derivation of the quintic NLS from many-body quantum dynamics in \(\mathbb T^2\), Dynamics of sound waves in an interacting Bose gas, On the mean-field approximation of many-boson dynamics, Convergence towards the Vlasov-Poisson equation from the \(N\)-fermionic Schrödinger equation, Dynamical Hartree-Fock-Bogoliubov approximation of interacting bosons

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1048088&oldid=13057292"