Convergence rate towards the fractional Hartree equation with singular potentials in higher Sobolev trace norms
From MaRDI portal
Publication:5019032
DOI10.1142/S0129055X2150029XzbMath1476.35214arXiv1805.01807OpenAlexW2802411584MaRDI QIDQ5019032
Publication date: 27 December 2021
Published in: Reviews in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.01807
PDEs in connection with quantum mechanics (35Q40) Many-body theory; quantum Hall effect (81V70) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Related Items
Propagation of Moments for Large Data and Semiclassical Limit to the Relativistic Vlasov Equation ⋮ On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate ⋮ On the time dependence of the rate of convergence towards Hartree dynamics for interacting bosons ⋮ Tracer particles coupled to an interacting boson gas
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Dynamics of sound waves in an interacting Bose gas
- On the blow-up solutions for the nonlinear fractional Schrödinger equation
- Focusing quantum many-body dynamics: the rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation
- On the rate of convergence for the mean field approximation of bosonic many-body quantum dynamics
- Short-range scattering of Hartree type fractional NLS
- Pair excitations and the mean field approximation of interacting Bosons. I
- Dynamical collapse of Boson stars
- Beyond mean field: on the role of pair excitations in the evolution of condensates
- Quantum many-body fluctuations around nonlinear Schrödinger dynamics
- 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
- Second-order corrections to mean field evolution of weakly interacting bosons. II
- Rate of convergence towards Hartree dynamics
- Remarks on some dispersive estimates
- A simple derivation of mean field limits for quantum systems
- Second-order corrections to mean field evolution for weakly interacting bosons in the case of three-body interactions
- On fractional Schrödinger equations in Sobolev spaces
- Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas
- 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 inhomogeneous Strichartz estimates for fractional Schrödinger equations and their applications
- On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
- Derivation of the time dependent Gross-Pitaevskii equation without positivity condition on the interaction
- Mean-field dynamics: Singular potentials and rate of convergence
- Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
- Mean field limit for bosons and infinite dimensional phase-space analysis
- Well-posedness for semi-relativistic Hartree equations of critical type
- Quantum dynamics with mean field interactions: a new approach
- Quantum fluctuations and rate of convergence towards mean field dynamics
- The Chandrasekhar theory of stellar collapse as the limit quantum mechanics
- The classical field limit of scattering theory for non-relativistic many- boson systems. II
- Fractional quantum mechanics and Lévy path integrals
- Weak coupling limit of the \(N\)-particle Schrödinger equation
- Mean-field quantum dynamics for a mixture of Bose-Einstein condensates
- Sharp threshold of blow-up and scattering for the fractional Hartree equation
- Bogoliubov correction to the mean-field dynamics of interacting bosons
- Asymptotic expansion of the mean-field approximation
- Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
- Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
- Rate of convergence towards semi-relativistic Hartree dynamics
- 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
- Bose-Einstein condensation for two dimensional bosons in the Gross-Pitaevskii regime
- On well-posedness for general hierarchy equations of Gross-Pitaevskii and Hartree type
- Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations
- Derivation of the Bogoliubov time evolution for a large volume 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
- On the mean-field approximation of many-boson dynamics
- Short-range scattering of Hartree type fractional NLS. II.
- Exact evolution versus mean field with second-order correction for bosons interacting via short-range two-body potential.
- Mean-field- and classical limit of many-body Schrödinger dynamics for bosons
- A note on the validity of Bogoliubov correction to mean-field dynamics
- Gross-Pitaevskii dynamics for Bose-Einstein condensates
- Norm approximation for many-body quantum dynamics: Focusing case in low dimensions
- On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamics
- Derivation of Hartree's theory for generic mean-field Bose systems
- Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in \(d=3\) based on spacetime norms
- Rigorous derivation of the cubic NLS in dimension one
- Bose-Einstein condensation beyond the Gross-Pitaevskii regime
- Evolution of the Boson gas at zero temperature: Mean-field limit and second-order correction
- Mean-field quantum dynamics with magnetic fields
- On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity
- Unconditional Uniqueness for the Cubic Gross-Pitaevskii Hierarchy via Quantum de Finetti
- Effective Evolution Equations from Quantum Dynamics
- A simple proof of convergence to the Hartree dynamics in Sobolev trace norms
- Pair excitations and the mean field approximation of interacting Bosons, II
- Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential
- Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
- Bose-Einstein Condensation and Liquid Helium
- Atomism and quantization
- Mean field dynamics of boson stars
- Fluctuations around Hartree states in the mean-field regime
- Rate of Convergence to Mean Field for Interacting Bosons
- Analysis of Fluctuations Around Non-linear Effective Dynamics
- Rate of convergence toward Hartree dynamics with singular interaction potential
- Another proof of BEC in the GP-limit
- A new second-order upper bound for the ground state energy of dilute Bose gases
- The excitation spectrum of the Bose gas in the Gross–Pitaevskii regime
- Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
- Bogoliubov corrections and trace norm convergence for the Hartree dynamics
- Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases
- Bogoliubov theory for dilute Bose gases: The Gross-Pitaevskii regime
- 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
- Derivation of the Hartree equation for compound Bose gases in the mean field limit
- Strichartz estimates in spherical coordinates
- Blowup for nonlinear wave equations describing boson stars
- On finite time blow-up for the mass-critical Hartree equations
- Mathematical concepts of quantum mechanics.
- A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas
