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Ground state
properties in the quasiclassical regime
Michele Correggi, Marco Falconi and Marco Olivieri |
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Vol. 16 (2023), No. 8, 1745–1798
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Abstract |
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We study the ground state energy and ground states of systems coupling nonrelativistic quantum particles and force-carrying Bose fields, such as radiation, in the quasiclassical 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 nonrelativistic particles, on the other hand, retain their microscopic features. We prove that the ground state energy of the fully microscopic model converges to that of a nonlinear quasiclassical 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 quasiclassical energy. |
Keywords
quasiclassical limit, interaction of matter and light,
semiclassical analysis
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Mathematical Subject Classification
Primary: 81Q20, 81T10
Secondary: 81Q05, 81Q10, 81S30, 81V10
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Milestones
Received: 13 November 2020
Revised: 2 November 2021
Accepted: 14 February 2022
Published: 16 October 2023
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Authors |
| Michele Correggi | |
| Dipartimento di Matematica Politecnico di Milano Milan Italy |
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| Marco Falconi | |
| Dipartimento di Matematica Politecnico di Milano Milan Italy |
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| Marco Olivieri | |
| Fakultät für Mathematik Karlsruhe Institut für Technologie Karlsruhe Germany |
Department of Mathematics Aarhus Universitet Aarhus Denmark |
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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