The nonlinear Schrödinger equation for orthonormal functions: existence of ground states
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Publication:2032399
DOI10.1007/s00205-021-01634-7zbMath1470.35328arXiv2002.04963OpenAlexW3153159091MaRDI QIDQ2032399
David Gontier, Faizan Q. Nazar, Mathieu Lewin
Publication date: 11 June 2021
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2002.04963
Spectral theory and eigenvalue problems for partial differential equations (35P99) NLS equations (nonlinear Schrödinger equations) (35Q55) Symmetry breaking in quantum theory (81R40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41) Fermionic systems in quantum theory (81V74)
Related Items (3)
The Lieb–Thirring inequalities: Recent results and open problems ⋮ Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates ⋮ The diatomic Hartree model at dissociation
Cites Work
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- Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials
- Strichartz inequality for orthonormal functions
- The Hartree equation for infinitely many particles. II: Dispersion and scattering in 2D
- On Schrödinger operators with inverse square potentials on the half-line
- Global well-posedness of the NLS system for infinitely many fermions
- Geometric methods for nonlinear many-body quantum systems
- The mathematics of the Bose gas and its condensation.
- Nonlinear Schrödinger equations and sharp interpolation estimates
- Nonlinear scalar field equations. I: Existence of a ground state
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- On a min-max procedure for the existence of a positive solution for certain scalar field equations in \({\mathbb{R}}^ N\)
- Proof of the ionization conjecture in a reduced Hartree-Fock model
- The crystallization conjecture: a review
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- Bound states for a coupled Schrödinger system
- Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs
- A new approach to the modeling of local defects in crystals: The reduced Hartree-Fock case
- An \(L^ p\) bound for the Riesz and Bessel potentials of orthonormal functions
- Localised solutions of Hartree equations for narrow-band crystals
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Error bound for the Hartree-Fock energy of atoms and molecules
- On the stability of the relativistic electron-positron field
- Accuracy of mean field approximations for atoms and molecules
- On the existence of a positive solution of semilinear elliptic equations in unbounded domains
- The multiconfiguration equations for atoms and molecules: charge quantization and existence of solutions
- Global existence versus finite time blowup dichotomy for the system of nonlinear Schrödinger equations
- Generalized Hartree-Fock theory and the Hubbard model
- A positive density analogue of the Lieb-Thirring inequality
- Stability of equilibria for a Hartree equation for random fields
- Symmetry breaking in the periodic Thomas-Fermi-Dirac-von Weizsäcker model
- The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities
- Stability of the Laughlin phase against long-range interactions
- The Hartree equation for infinitely many particles. I: Well-posedness theory
- Bound and ground states of coupled nonlinear Schrödinger equations
- On the Strichartz estimates for orthonormal systems of initial data with regularity
- On the mass concentration for Bose-Einstein condensates with attractive interactions
- Zeros of the modified Hankel function
- Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
- Ground state of \(N\) coupled nonlinear Schrödinger equations in \(\mathbb R^n\), \(n \leq 3\)
- Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation
- Uniqueness of Positive Radial Solutions of Δu + f(u) = 0 in ℝ n , II
- On the Analyticity of the Solutions of Analytic Non-Linear Elliptic Systems of Partial Differential Equations: Part I. Analyticity in the Interior
- The Stability of Matter in Quantum Mechanics
- Modulational Stability of Ground States of Nonlinear Schrödinger Equations
- A ecessary and Sufficient Condition for The Stability of General molecular Systems
- Asymptotic decay of the solution of a second-order elliptic equation in an unbounded domain. Applications to the spectral properties of a Hamiltonian
- Binding of atoms and stability of molecules in hartree and thomas—fermi type theories
- Binding of atoms and stability of molecules in hartree and thomas-fermi type theories.
- Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates
- The n -component nonlinear Schrödinger equations: dark–bright mixed N - and high-order solitons and breathers, and dynamics
- Symmetry breaking regime in the nonlinear Hartree equation
- On the thermodynamic limit for Hartree-Fock type models
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