Second quantized reduced Bloch equations and the exact solutions for pairing Hamiltonian
- 作者：Wei ; Liqiang ; Sun ; Chiachung ; Zeng ; Zonghao
- 关键词：05.30-d ; 71.10.-w ; 71.10.Fd ; 71.10.Li ; Second quantization ; Reduced Bloch equations ; Reduced density matrix ; Pairing Hamiltonian ; Symplectic symmetry ; Contraction operator
- 刊名：Annals of Physics
- 出版年：2004
- 期刊代码：63_00034916
- 类别：mt
- 出版时间：September, 2004
- 卷：313
- 期：1
- 页码：1-15
- 文件大小：243 K
摘要
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.