We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled Klein–Gordon–Schrödinger equation. Also, we show that the ground state energy level of N nucleons, when N is large and the meson field approaches its classical value, is given by the infimum of the classical energy functional at a fixed density of particles. Our study relies on a recently elaborated approach for mean field theory and uses Wigner measures.
Ammari, Z., Falconi, M. (2014). Wigner Measures Approach to the Classical Limit of the Nelson Model: Convergence of Dynamics and Ground State Energy. JOURNAL OF STATISTICAL PHYSICS, 157(2), 330-362 [10.1007/s10955-014-1079-7].
Wigner Measures Approach to the Classical Limit of the Nelson Model: Convergence of Dynamics and Ground State Energy
Falconi M.
2014-01-01
Abstract
We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled Klein–Gordon–Schrödinger equation. Also, we show that the ground state energy level of N nucleons, when N is large and the meson field approaches its classical value, is given by the infimum of the classical energy functional at a fixed density of particles. Our study relies on a recently elaborated approach for mean field theory and uses Wigner measures.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.