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Physica A Statistical Mechanics and its Applications

Analysis of the reservoir model in thermo-field dynamics

Y. Georgelin, Y. Leblanc

Published Mar 1, 1991• 0 citations
Publisher
DOI
10.1016/0378-4371(91)90301-r

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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.
By analyzing the characters of thermo field dynamics, which is proposed by Takahashi and Umezawa, we find that a new physical state, named the thermo-invariant coherent state, should exist in thermal equilibrium. This state not only maintains the whole energy of the system and the reservoir but is also a coherent state. We find its explicit form, its relation to the thermal coherent state and the thermal entangled state. When the whole system is in this state, annihilating a quantum of the system and in the meanwhile annihilating a hole with negative energy in the reservoir will not change the whole energy.