Second quantized reduced Bloch equations and the exact solutions for pairing Hamiltonian

作者：Wei LQ^*; Sun CC; Zeng ZG

来源：Annals of Physics, 2004, 313(1): 1-15.

DOI：10.1016/j.aop.2004.04.007

• second quantization
• reduced Bloch equations
• reduced density matrix
• pairing Hamiltonian
• symplectic symmetry
• contraction operator

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.

• 出版日期2004-9
• 单位中国科学院生物物理研究所; 吉林大学