Derivation of the time dependent Gross-Pitaevskii equation in two dimensions
From MaRDI portal
Publication:2008947
DOI10.1007/s00220-019-03599-xzbMath1442.81065arXiv1608.05326OpenAlexW2513808612WikidataQ97523931 ScholiaQ97523931MaRDI QIDQ2008947
Peter Pickl, Maximilian Jeblick, Nikolai Leopold
Publication date: 26 November 2019
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1608.05326
Interacting particle systems in time-dependent statistical mechanics (82C22) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Many-body theory; quantum Hall effect (81V70)
Related Items
Mean field derivation of DNLS from the Bose-Hubbard model, The mean-field limit of the Lieb-Liniger model, Derivation of the Landau-Pekar equations in a many-body mean-field limit, Beyond Bogoliubov dynamics, Derivation of the 2d Gross-Pitaevskii equation for strongly confined 3d bosons, Improved stability for 2D attractive Bose gases, On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate, Derivation of the Maxwell--Schrödinger Equations from the Pauli--Fierz Hamiltonian, 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, Higher order corrections to the mean-field description of the dynamics of interacting bosons, Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger, Bose-Einstein condensation for two dimensional bosons in the Gross-Pitaevskii regime, Derivation of the Bogoliubov time evolution for a large volume mean-field limit, Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates
Cites Work
- Unnamed Item
- 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
- Pair excitations and the mean field approximation of interacting Bosons. I
- Quantum many-body fluctuations around nonlinear Schrödinger dynamics
- Focusing quantum many-body dynamics. II: The rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation from 3D
- The mathematics of the Bose gas and its condensation.
- Second-order corrections to mean field evolution of weakly interacting bosons. II
- A simple derivation of mean field limits for quantum systems
- The NLS limit for Bosons in a quantum waveguide
- Derivation of the cubic nonlinear Schrödinger equation from quantum dynamics of many-body systems
- 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
- Quantum fluctuations and rate of convergence towards mean field dynamics
- A new method and a new scaling for deriving fermionic mean-field dynamics
- Bogoliubov correction to the mean-field dynamics of interacting bosons
- Derivation of the 1d Gross-Pitaevskii equation from the 3d quantum many-body dynamics of strongly confined bosons
- Derivation of the time dependent two dimensional focusing NLS equation
- Mean-field dynamics for the Nelson model with fermions
- Fluctuations of \(N\)-particle quantum dynamics around the nonlinear Schrödinger equation
- Large time behavior in nonlinear Schrödinger equations with time dependent potential
- Exact evolution versus mean field with second-order correction for bosons interacting via short-range two-body potential.
- A note on the validity of Bogoliubov correction to mean-field dynamics
- Gross-Pitaevskii dynamics for Bose-Einstein condensates
- Mean-field limits of particles in interaction with quantized radiation fields
- 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
- Effective Evolution Equations from Quantum Dynamics
- A simple proof of convergence to the Hartree dynamics in Sobolev trace norms
- A note on 2D focusing many-boson systems
- 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
- Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate
- Fluctuations around Hartree states in the mean-field regime
- The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-Body Evolution
- Adiabatic Approximation of the Schrödinger--Poisson System with a Partial Confinement
- Bogoliubov corrections and trace norm convergence for the Hartree dynamics
- Derivation of the time dependent Gross–Pitaevskii equation with external fields
- Quantitative Derivation of the Gross‐Pitaevskii Equation
- Derivation of the 1d nonlinear Schrödinger equation from the 3d quantum many-body dynamics of strongly confined bosons
- The ground state energy of a dilute two-dimensional Bose gas.
- A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas