Ground State Properties in the Quasi-Classical Regime
arXiv:2007.09442 · doi:10.2140/apde.2023.16.1745
Abstract
We study the ground state energy and ground states of systems coupling non-relativistic quantum particles and force-carrying Bose fields, such as radiation, in the quasi-classical approximation. The latter is very useful whenever the force-carrying field has a very large number of excitations,and thus behaves in a semiclassical way, while the non-relativistic particles, on the other hand, retain their microscopic features. We prove that the ground state energy of the fully microscopic model converges to the one of a nonlinear quasi-classical functional depending on both the particles' wave function and the classical configuration of the field. Equivalently, this energy can be interpreted as the lowest energy of a Pekar-like functional with an effective nonlinear interaction for the particles only. If the particles are confined, the ground state of the microscopic system converges as well, to a probability measure concentrated on the set of minimizers of the quasi-classical energy.
arXiv comment52 pages, pdfLaTeX
References in corpus (25)
- Ground States in Non-relativistic Quantum Electrodynamics
- Erratum: Exact Ground State Energy of the Strong-Coupling Polaron
- On the self-adjointness and domain of Pauli-Fierz type Hamiltonians
- Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
- Mean field limit for bosons and propagation of Wigner measures
- Dynamics of a strongly coupled polaron
- Analyticity of The Ground State Energy For Massless Nelson Models
- On the dynamics of polarons in the strong-coupling limit
- Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit
- Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy
- Magnetic Schrödinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models
- Infrared problem for the Nelson model on static space-times
- One Particle (improper) states and Scattering States in Nelson's Massless Model
- Divergence of the effective mass of a polaron in the strong coupling limit
- Self-Adjointness criterion for operators in Fock spaces
- Concentration of cylindrical Wigner measures
- Ground states and associated path measures in the renormalized Nelson model
- Derivation of the Landau-Pekar equations in a many-body mean-field limit
- A note on the Fröhlich dynamics in the strong coupling limit
- Quasi-Classical Dynamics
- Pauli-Fierz type operators with singular electromagnetic potentials on general domains
- Hamiltonian systems and semiclassical dynamics for interacting spins in QED
- Microscopic Derivation of Time-dependent Point Interactions
- A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations
- Infinite dimensional semiclassical analysis and applications to a model in NMR