ON THE MAGNETIC PEKAR FUNCTIONAL AND THE EXISTENCE OF BIPOLARONS

DOI10.1142/S0129055X12500146zbMath1250.49042arXiv1111.1624OpenAlexW2144421682MaRDI QIDQ2911999

Marcel Griesemer, Fabian Hantsch, D. Wellig

Publication date: 13 September 2012

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

Full work available at URL: https://arxiv.org/abs/1111.1624

zbMATH Keywords

nonlinear Schrödinger equationconcentration compactness principleChoquard equationSchrödinger-Newton equationbinding of polaronsPekar-Tomasevich functional

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Many-body theory; quantum Hall effect (81V70) Existence theories for optimal control problems involving partial differential equations (49J20) Variational principles of physics (49S05)

Related Items

Symmetry of bipolaron bound states for small Coulomb repulsion ⋮ Monotonicity of the polaron energy. II: General theory of operator monotonicity ⋮ Quasi-classical ground states. I: Linearly coupled Pauli-Fierz Hamiltonians ⋮ Multipolarons in a constant magnetic field ⋮ A guide to the Choquard equation ⋮ Monotonicity of the polaron energy ⋮ On the strong coupling limit of many-polaron systems in electromagnetic fields ⋮ The ground state energy of a polaron in a strong magnetic field

Cites Work

• Multiple solutions to a magnetic nonlinear Choquard equation
• Geometric methods for nonlinear many-body quantum systems
• Schrödinger operators with magnetic fields. I: General interactions
• Exact ground state energy of the strong-coupling polaron
• Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
• The bipolaron in the strong coupling limit
• Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities
• Asymptotics for the polaron
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation