The time-dependent Hartree-Fock-Bogoliubov equations for bosons

DOI10.1007/s00028-022-00799-2OpenAlexW2277667450WikidataQ126009880 ScholiaQ126009880MaRDI QIDQ2140841

Volker Bach, Thomas Chen, Sébastien Breteaux, Jürg Fröhlich, Israel Michael Sigal

Publication date: 23 May 2022

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.05171

zbMATH Keywords

Bose-Einstein condensateHartree-Fock-Bogoliubov equationsquantum Bose gases

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Statistical mechanics of superconductors (82D55) PDEs in connection with quantum mechanics (35Q40) Many-body theory; quantum Hall effect (81V70) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Statistical mechanics of gases (82D05) Bosonic systems in quantum theory (81V73)

Related Items (9)

Mean field dynamics of a quantum tracer particle interacting with a boson gas ⋮ Beyond mean-field: Condensate coupled with pair excitations ⋮ On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate ⋮ The Dirac-Frenkel principle for reduced density matrices, and the Bogoliubov-de Gennes equations ⋮ Derivation of the Bogoliubov time evolution for a large volume mean-field limit ⋮ Bogoliubov corrections and trace norm convergence for the Hartree dynamics ⋮ Evolution of the Boson gas at zero temperature: Mean-field limit and second-order correction ⋮ Uniform in N estimates for a Bosonic system of Hartree–Fock–Bogoliubov type ⋮ Differential equations of quantum mechanics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
• Pair excitations and the mean field approximation of interacting Bosons. I
• Beyond mean field: on the role of pair excitations in the evolution of condensates
• An existence proof for the Hartree-Fock time-dependent problem with bounded two-body interaction
• The time-dependent Hartree-Fock equations with Coulomb two-body interaction
• The Bogoliubov free energy functional. II: The dilute limit
• The Bogoliubov free energy functional. I: Existence of minimizers and phase diagram
• Bogoliubov correction to the mean-field dynamics of interacting bosons
• The Dirac-Frenkel principle for reduced density matrices, and the Bogoliubov-de Gennes equations
• Generalized Hartree-Fock theory and the Hubbard model
• Theory of non-equilibrium stationary states as a theory of resonances
• Non-linear semi-groups
• On quasifree states of the canonical commutation relations. I
• Time-ordered operator products of sharp-time quadratic forms
• The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases
• Propagation of chaos for many-boson systems in one dimension with a point pair-interaction
• A note on 2D focusing many-boson systems
• Pair excitations and the mean field approximation of interacting Bosons, II
• Fluctuations around Hartree states in the mean-field regime
• PROPERTIES OF NONFREENESS: AN ENTROPY MEASURE OF ELECTRON CORRELATION
• Global existence of solutions to the Cauchy problem for time-dependent Hartree equations
• Generalization of Lieb's variational principle to Bogoliubov–Hartree–Fock theory
• Linear Symmetries of Free Boson Fields
• Mathematical concepts of quantum mechanics.

This page was built for publication: The time-dependent Hartree-Fock-Bogoliubov equations for bosons