The Dirac-Frenkel principle for reduced density matrices, and the Bogoliubov-de Gennes equations
From MaRDI portal
Publication:1745377
DOI10.1007/s00023-018-0644-zzbMath1390.81757arXiv1706.03082OpenAlexW2625874396MaRDI QIDQ1745377
Jérémy Sok, Niels Benedikter, Jan Philip Solovej
Publication date: 17 April 2018
Published in: Annales Henri Poincaré (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1706.03082
reduced density matriceseffective evolution equationsBogoliubov-de Gennes equationsDirac-Frenkel principleHartree-Fock-Bogoliubov equations
Many-body theory; quantum Hall effect (81V70) Quantum state spaces, operational and probabilistic concepts (81P16)
Related Items
Effective dynamics of interacting fermions from semiclassical theory to the random phase approximation, Mean field derivation of DNLS from the Bose-Hubbard model, Bosonization of fermionic many-body dynamics, Joint quantum–classical Hamilton variational principle in the phase space*, The time-dependent Hartree-Fock-Bogoliubov equations for bosons, Decay in energy space for the solution of fourth-order Hartree-Fock equations with general non-local interactions, Correlation energy of a weakly interacting Fermi gas with large interaction potential, On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate, On some rigorous aspects of fragmented condensation, Vortex lattices and the Bogoliubov-de Gennes equations, Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime, Bosonic collective excitations in Fermi gases, Mean-field dynamics for the Nelson model with fermions, Uniform in \(N\) global well-posedness of the time-dependent Hartree-Fock-Bogoliubov equations in \(\mathbb {R}^{1+1}\), Decay and scattering in energy space for the solution of weakly coupled Schrödinger-Choquard and Hartree-Fock equations, Correlation energy of a weakly interacting Fermi gas, Uniform in N estimates for a Bosonic system of Hartree–Fock–Bogoliubov type, Global estimates for the Hartree–Fock–Bogoliubov equations, Differential equations of quantum mechanics
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Pair excitations and the mean field approximation of interacting Bosons. I
- Quantum many-body fluctuations around nonlinear Schrödinger dynamics
- On the existence of solutions to time-dependent Hartree-Fock equations
- Second-order corrections to mean field evolution of weakly interacting bosons. I
- On blowup for time-dependent generalized Hartree-Fock equations
- Second-order corrections to mean field evolution of weakly interacting bosons. II
- Rate of convergence towards Hartree dynamics
- A microscopic derivation of the time-dependent Hartree-Fock equation with Coulomb two-body interaction
- A simple derivation of mean field limits for quantum systems
- Rate of convergence towards the Hartree-von Neumann limit in the mean-field regime
- Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons
- On the mean-field limit of bosons with Coulomb two-body interaction
- Derivation of the cubic nonlinear Schrödinger equation from quantum dynamics of many-body systems
- A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on \(\mathbb{T}^3\) from the dynamics of many-body quantum systems
- Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction
- From quantum to classical molecular dynamics: Reduced models and numerical analysis.
- Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs
- 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
- 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
- Mean field dynamics of fermions and the time-dependent Hartree-Fock equation
- Weak coupling limit of the \(N\)-particle Schrödinger equation
- A new method and a new scaling for deriving fermionic mean-field dynamics
- Bogoliubov correction to the mean-field dynamics of interacting bosons
- Nonlinear Hartree equation as the mean field limit of weakly coupled fermions
- Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
- The time-dependent Hartree-Fock-Bogoliubov equations for bosons
- Kato's theorem on the integration of non-autonomous linear evolution equations
- Mean field evolution of fermions with Coulomb interaction
- Non-linear semi-groups
- Two theorems about \(C_p\)
- Dynamics of Bose-Einstein condensates of fermion pairs in the low density limit of BCS theory
- Rigorous derivation of the cubic NLS in dimension one
- Mean-Field Evolution of Fermionic Mixed States
- 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
- On the Vlasov hierarchy
- Global existence of solutions to the Cauchy problem for time-dependent Hartree equations
- On the dynamics of polarons in the strong-coupling limit
- Hartree corrections in a mean-field limit for fermions with Coulomb interaction
- Derivation of the time dependent Gross–Pitaevskii equation with external fields
- Quantitative Derivation of the Gross‐Pitaevskii Equation
- Mean-field dynamics of fermions with relativistic dispersion
- Mean-field evolution of fermionic systems
