Second quantized reduced Bloch equations and the exact solutions for pairing Hamiltonian
Abstract
In this article, we present a set of hierarchy Bloch equations for the reduced density operators in either canonical or grand canonical ensembles in the occupation number representation. They provide a convenient tool for studying the equilibrium quantum statistical mechanics for some model systems. As an example of their applications, we solve the equations for the model system with a pairing Hamiltonian. With the aid of its symplectic group symmetry, we obtain the statistical reduced density matrices with different orders. As a special instance for the solutions, we also get the reduced density matrices of the ground state for a superconductor.
 Publication:

Annals of Physics
 Pub Date:
 September 2004
 DOI:
 10.1016/j.aop.2004.04.007
 arXiv:
 arXiv:condmat/0311288
 Bibcode:
 2004AnPhy.313....1W
 Keywords:

 05.30d;
 71.10.w;
 71.10.Fd;
 71.10.Li;
 Theories and models of manyelectron systems;
 Lattice fermion models;
 Excited states and pairing interactions in model systems;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Annual of Physics 313, 1 (2004)