We study the quasi-classical limit of the Pauli–Fierz model: the system is composed of finitely many non-relativistic charged particles interacting with a bosonic radiation field. We trace out the degrees of freedom of the field, and consider the classical limit of the latter. We prove that the partial trace of the full Hamiltonian converges, in resolvent sense, to an effective Schrödinger operator with magnetic field and a corrective electric potential that depends on the field configuration. Furthermore, we prove the convergence of the ground state energy of the microscopic system to the infimum over all possible classical field configurations of the ground state energy of the effective Schrödinger operator.

Magnetic Schrödinger operators as the quasi-classical limit of Pauli–Fierz-type models

Correggi M.;Falconi M.;
2019-01-01

Abstract

We study the quasi-classical limit of the Pauli–Fierz model: the system is composed of finitely many non-relativistic charged particles interacting with a bosonic radiation field. We trace out the degrees of freedom of the field, and consider the classical limit of the latter. We prove that the partial trace of the full Hamiltonian converges, in resolvent sense, to an effective Schrödinger operator with magnetic field and a corrective electric potential that depends on the field configuration. Furthermore, we prove the convergence of the ground state energy of the microscopic system to the infimum over all possible classical field configurations of the ground state energy of the effective Schrödinger operator.
Magnetic Laplacians; Magnetic Schrödinger operators; Pauli–Fierz model; Quasi-classical limit
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1134363
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