Mean-field Dynamics for the Nelson Model with Fermions
arXiv:1807.06781 · doi:10.1007/s00023-019-00828-w
Abstract
We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schroedinger-Klein-Gordon equations.
arXiv comment31 pages; v3: several minor improvements
References in corpus (17)
- Mean-field Evolution of Fermionic Systems
- Mean field evolution of fermions with Coulomb interaction
- From the Hartree dynamics to the Vlasov equation
- Mean-Field Dynamics of Fermions with Relativistic Dispersion
- A New Method and a New Scaling For Deriving Fermionic Mean-field Dynamics
- Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction
- The Dirac-Frenkel Principle for Reduced Density Matrices, and the Bogoliubov-de-Gennes Equations
- Classical limit of the Nelson model with cut off
- Dynamics of a strongly coupled polaron
- On the dynamics of polarons in the strong-coupling limit
- Derivation of an effective evolution equation for a strongly coupled polaron
- Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit
- Well-posedness of non-autonomous linear evolution equations in uniformly convex spaces
- Accuracy of the time-dependent Hartree-Fock approximation for uncorrelated initial states
- Effective N-body dynamics for the massless Nelson model and adiabatic decoupling without spectral gap
- Hartree Corrections in a Mean-field Limit for Fermions with Coulomb Interaction
- Mean-field limits of particles in interaction with quantized radiation fields
Cited by in corpus (5)
- Derivation of the Time Dependent Gross-Pitaevskii Equation in Two Dimensions
- The Landau-Pekar equations: Adiabatic theorem and accuracy
- Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
- Derivation of the Landau-Pekar equations in a many-body mean-field limit
- Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model