On the dynamics of polarons in the strong-coupling limit

DOI10.1142/S0129055X17500301zbMath1377.81264arXiv1612.00395MaRDI QIDQ4595001

Marcel Griesemer

Publication date: 27 November 2017

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

Full work available at URL: https://arxiv.org/abs/1612.00395

zbMATH Keywords

Dirac-Frenkel variational principleLandau-Pekar equationsstrong-coupling polarondynamics of polarons

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Quantum optics (81V80) NLS equations (nonlinear Schrödinger equations) (35Q55) Statistical mechanics of solids (82D20)

Related Items (19)

Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field ⋮ A note on the Fröhlich dynamics in the strong coupling limit ⋮ The effective mass problem for the Landau–Pekar equations ⋮ Derivation of the Landau-Pekar equations in a many-body mean-field limit ⋮ Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron ⋮ Norm approximation for the Fröhlich dynamics in the mean-field regime ⋮ Bogoliubov dynamics and higher-order corrections for the regularized Nelson model ⋮ Effective potentials generated by field interaction in the quasi-classical limit ⋮ Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron ⋮ Ground state properties in the quasiclassical regime ⋮ Quasi-classical dynamics ⋮ Derivation of the Maxwell--Schrödinger Equations from the Pauli--Fierz Hamiltonian ⋮ The Dirac-Frenkel principle for reduced density matrices, and the Bogoliubov-de Gennes equations ⋮ The polaron at strong coupling ⋮ Mean-field dynamics for the Nelson model with fermions ⋮ Emergence of Time-Dependent Point Interactions in Polaron Models ⋮ Bogoliubov theory for many-body quantum systems ⋮ The Landau-Pekar equations: adiabatic theorem and accuracy ⋮ A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations

Cites Work

• Well-posedness of non-autonomous linear evolution equations for generators whose commutators are scalar
• Dynamics of a strongly coupled polaron
• Derivation of an effective evolution equation for a strongly coupled polaron
• Geometric methods for nonlinear many-body quantum systems
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• From quantum to classical molecular dynamics: Reduced models and numerical analysis.
• Exact ground state energy of the strong-coupling polaron
• Multipolarons in a constant magnetic field
• On the dynamics of the mean-field polaron in the high-frequency limit
• On the time evolution of the mean-field polaron
• Self-adjointness and domain of the Fröhlich Hamiltonian
• Asymptotics for the polaron
• The Choquard equation and related questions
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

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