Stochastic Models for Many-Body Systems, Vol. 1: Infinite Systems in Thermal Equilibrium (Classic Reprint) - Softcover
Synopsis
New approaches to infinite quantum systems that stay manageable.
This book develops stochastic models for many-body problems, offering closed equations for propagators and key thermodynamic quantities in the infinite-system limit. It shows how random parameters can be used to sum infinite classes of terms and reveal predictable, controllable behavior in complex quantum systems.
Two principal model families are introduced: ladder and ring, each capturing important classes of diagrams from perturbation theory while also incorporating self-energy corrections that affect damping of excitations. The discussion covers both distinguishable particles and indistinguishable particles (fermions and bosons), and it explains how different modeling choices lead to shared thermodynamic outcomes in the classical limit. A temperature-domain propagator formalism, rooted in Matsubara-type methods, is developed alongside Appendix-style generalized models for broader applicability, including non-equilibrium scenarios.What you’ll experience
- Clear explanation of ladder and ring stochastic models and their physical meaning
- Connections between Hartree-Fock approximations and their random-coupling extensions
- Closed integral equations for propagators that determine mean energies and occupation numbers
- Discussion of convergence questions and the limits of perturbation theory in infinite systems
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