Reduced Density Matrices: Coulson's Challenge

ISBN-13: 9783540671480 / Angielski / Miękka / 2000 / 282 str.

A. John Coleman; V. I. Yukalov

Opis

The authors demonstrate that the essential information about order in, and energy levels of physical systems is encapsulated in the second order reduced density matrix. They have discovered an algorithm to obtain a reasonable accurate expression for the 2-matrix of an N-particle state to make nearly all properties of matter which are of interest to chemists and physicists accessible.

Spis treści

1 Basic properties.- 1.1 Reduced Density Matrices.- 1.2 N-representability.- 1.3 Norbs, Nags and Least Squares.- 1.4 Fock Space.- 1.5 Reduced Density Matrices on Fock Space.- 1.6 Unitary Invariance.- 1.7 Notes.- 1.8 Exercises.- 2 N-Representability.- 2.1 The p-rank of a State.- 2.2 Convexity.- 2.3 Ensemble N-representability.- 2.4 A Family of Convex Surfaces.- 2.5 Parameterizing.- 2.6 The Total Energy.- 2.7 The One-matrix.- 2.8 Notes.- 2.9 Exercises.- 2.10 Appendix — Figures for Chapter 2.- 3 Correlation.- 3.1 Sasaki’s Formula.- 3.2 Bounds on for fermions.- 3.3 Necessary Conditions.- 3.4 A Universal Fermion Model.- 3.5 Strong Orthogonality.- 3.6 Unitary Decomposition.- 3.7 Reduced Hamiltonian Orbitals.- 3.7.1 For LiH.- 3.7.2 For H2O.- 3.8 Intracules, extracules and Statistics.- 3.9 Notes for Chapter 3.- 3.10 Exercises for Chapter 3.- 3.11 Appendix — The Pfaffian.- 4 Generalized AGP.- 4.1 Canonical form for g(12).- 4.2 Properties of GAGP.- 4.3 Extreme AGP.- 4.4 Scope of GAGP.- 4.5 Error Control.- 4.6 The GAGP Energy.- 4.7 Critical values of E.- 4.8 Hartree-Fock-Bogolubov Equations.- 4.9 Notes.- 4.10 Exercises.- 5 Boson Systems.- 5.1 Yang’s Paper.- 5.2 Order Indices.- 5.3 Green’s Functions and Propagators.- 5.4 Bose Condensation.- 5.5 Mesoscopic Condensation.- 5.6 Bose Liquid.- 5.7 Collective Excitations.- 5.8 Notes.- 6 Fermion Systems.- 6.1 The Superconducting Transition.- 6.2 Heterophase Superconductor.- 6.3 Notes.- 6.4 Figures.- 7 Coulson’s Challenge.- 7.1 The Reduced Hamiltonian.- 7.2 Pairon Distribution function.- 7.3 Facing the Challenge!.- 7.4 Notes.

Blurb

The authors demonstrate that the essential information about order, and energy levels of physical systems is encapsulated in the second order reduced density matrix. They have discovered an algorithm to obtain a reasonable accurate expression for the 2-matrix of an N-particle state to make nearly all properties of matter which are of interest to chemists and physicists accessible.