THE EFFECTIVE POTENTIAL AND EFFECTIVE HAMILTONIAN IN QUANTUM-STATISTICAL MECHANICS

An overview on the theoretic formalism and up to date applications in quantum condensed matter physics of the effective potential and effect ive Hamiltonian methods is given. The main steps of their unified deri vation by the so-called pure quantum self-consistent harmonic approxim ation (PQSCHA) are reported and explained. What makes this framework a ttractive is its easy implementation as well as the great simplificati on in obtaining results for the statistical mechanics of complicated q uantum systems. Indeed, for a given quantum system the PQSCHA yields a n effective system, i.e. an effective classical Hamiltonian with depen dence on ($) over bar h and beta and classical-like expressions for th e averages of observables, that has to be studied by classical methods . Anharmonic single-particle systems are analysed in order to get insi ght into the physical meaning of the PQSCHA, and its extension to the investigation of realistic many-body systems is pursued afterwards. Th e power of this approach is demonstrated through a collection of appli cations in different fields, such as soliton theory, rare gas crystals and magnetism. Eventually, the PQSCHA allows us also to approach quan tum dynamical properties.