JournalsjstVol. 9, No. 4pp. 1287–1325

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

  • Michele Correggi

    Università di Roma La Sapienza, Italy
  • Marco Falconi

    Universität Zürich, Switzerland
  • Marco Olivieri

    Università di Roma La Sapienza, Italy
Magnetic Schrödinger operators as the quasi-classical limit of Pauli–Fierz-type models cover
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Abstract

We study the quasi-classical limit of the Pauli–Fierz model: the system is composed of finitelymany non-relativistic charged particles interactingwith 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 systemto the infimum over all possible classical field configurations of the ground state energy of the effective Schrödinger operator.

Cite this article

Michele Correggi, Marco Falconi, Marco Olivieri, Magnetic Schrödinger operators as the quasi-classical limit of Pauli–Fierz-type models. J. Spectr. Theory 9 (2019), no. 4, pp. 1287–1325

DOI 10.4171/JST/277