摘要
Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state （TVS） for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann-Feynman theorem and the entroy variation in the context of the TVS.
Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state （TVS） for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann-Feynman theorem and the entroy variation in the context of the TVS.
基金
supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11264018)
the Natural Science Foundation of Jiangxi Province, China (Grant Nos. 20132BAB212006, 20114BAB202004, and 2009GZW0006)
the Research Foundation of the Education Department of Jiangxi Province, China (Grant No. GJJ12171)
the Open Foundation of the Key Laboratory of Optoelectronic and Telecommunication of Jiangxi Province, China (Grant No. 2013004)
