Infinite-volume limit of continuous n-particle quantum systems

Abstract

The Feynman–Kac theorem is applied in order to establish the infinite-volume limit behaviour of the free energy per particle of continuous n-particle quantum systems with bounded separable 2-body interactions defined in the configuration space of particle positions. The mean-field character of such systems is demonstrated. A similar technique is applied to n-particle quantum systems with separable interactions defined in the space of particle momenta and spins. Three examples of systems with separable interactions are given and solved, one of which deals with an electron gas interacting with localized impurity spins in a dilute magnetic alloy (DMA) and extension of Kondo’s resistivity formula for DMA to temperatures close to 0 K. Most of the results are generalizations or more detailed presentations of those published earlier.