Non-Equilibrium Thermo-Field Dynamics for a Fourth-Order Hamiltonian

The non-equilibrium thermo-field dynamics proposed by Arimitsu and Umezawa are generalized to the case of a fourth-order unperturbed Hamiltonian which includes not only a second-order (quadratic) part but also a fourth-order part. Fujita's analysis for effects of the initial particle correlation of a quantum gas is proved generally in terms of TFD. The forms of the quasi-particle operators for a semi-free boson field are derived. It is shown that the energies and life-times of the quasi-particles depend on the adiabatic boson-reservoir interaction which leads to the fourth-order part of the unperturbed Hamiltonian. The form of the two-point Green's function for the semi-free boson field is evaluated. A form of the admittance for a boson system interacting with its heat reservoir, which includes effects of the initial correlation and memory, is derived using the TCLE method formulated in terms of the generalized non-equilibrium thermo-field dynamics. A calculation method of the higher-order parts of the admittance in powers of the boson-boson interaction is given. Furthermore, a calculation method of the perturbation expansions of the two-point Green's function for the boson system is given.