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.

Correggi, M., Falconi, M. (2018). Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit. ANNALES HENRI POINCARE', 19(1), 189-235 [10.1007/s00023-017-0612-z].

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

Correggi M.;Falconi M.
2018-01-01

Abstract

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.
Correggi, M., Falconi, M. (2018). Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit. ANNALES HENRI POINCARE', 19(1), 189-235 [10.1007/s00023-017-0612-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/355106
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