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 Schr\"odinger 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 Schr\"odinger operator.

Magnetic Schrödinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models / Correggi, M.; Falconi, M.; Olivieri, M.. - In: JOURNAL OF SPECTRAL THEORY. - ISSN 1664-039X. - (2017).

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

M. Correggi;M. Olivieri
2017

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 Schr\"odinger 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 Schr\"odinger operator.
2017
Mathematical Physics; Mathematical Physics; Mathematics - Mathematical Physics
01 Pubblicazione su rivista::01a Articolo in rivista
Magnetic Schrödinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models / Correggi, M.; Falconi, M.; Olivieri, M.. - In: JOURNAL OF SPECTRAL THEORY. - ISSN 1664-039X. - (2017).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1246063
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