Magnetic Schrödinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models


JST 9(4) 1287-1325, 2019

The article is available at EMS Publishing House (under subscritpion).

arXiv 1711.07413

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The bibtex entry for the article can be downloaded here.


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.