• DOI:10.1007/s00023-017-0612-z
• Corpus ID: 119126339

Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit

@article{Correggi2017EffectivePG,
  title={Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit},
  author={Michele Correggi and Marco Falconi},
  journal={Annales Henri Poincar{\'e}},
  year={2017},
  volume={19},
  pages={189-235}
}

• M. Correggi, M. Falconi
• Published 5 January 2017
• Mathematics, Physics
• Annales Henri Poincaré

We study the quasi-classical limit of a quantum system composed of finitely many nonrelativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes classical and the corresponding degrees of freedom are traced out, the effective Hamiltonian of the particles converges in resolvent sense to a self-adjoint Schrödinger operator with an additional potential, depending on the state of the field. Moreover, we explicitly derive the expression of such a potential for a large class of field states and show that, for certain special sequences of states, the effective potential is trapping. In addition, we prove convergence of the ground-state energy of the full system to a suitable effective variational problem involving the classical state of the field.