2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/24527On the grounds of a Feynman-Kac--type formula for Hamiltonian lattice systems we derive analytical expressions for the matrix elements of the evolution operator. These expressions are valid at long times when a central limit theorem applies. As a remarkable result we find that the ground-state energy as well as all the correlation functions in the ground state are determined semi-analytically by solving a simple scalar equation. Furthermore, explicit solutions of this equation are obtained in the noninteracting case.Other Condensed MatterHigh Energy Physics - LatticeMathematical PhysicsProbabilityQuantum Physicstext