Prog. Theor. Phys. Vol. 79 No. 3 (1988) pp. 627-644
An Effective Hamiltonian in Nonequilibrium Thermo Field Dynamics with a Reservoir
Dipartimento di Fisica Teorica, e sue Metodologie per le Scienze Applicate, Università di Salerno, 84100 Salerno
(Received May 6, 1986)
General properties of an effective Hamiltonian in thermo field dynamics, which includes reservoir effects through coarse graining, are investigated. The necessary and sufficient conditions for the effective Hamiltonian to describe the reservoir effect are obtained. The final canonical distribution is discussed with relation to each given interaction. The result gives a quick and easy guide to construct an effective Hamiltonian and to identify the final equilibrium state.
DOI : 10.1143/PTP.79.627
- H. Umezawa, H. Matsumoto and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland Pub., Amsterdam-New York-London, 1982).
H. Matsumoto, in Progress in Quantum Field Theory, ed. H. Ezawa and S. Kamefuchi (North-Holland, Amsterdam, 1986), p. 171.
- T. Arimitsu and H. Umezawa, Prog. Theor. Phys. 74 (1985), 429[PTP]; ibid. 77 (1987), 32[PTP].
- H. Matsumoto, Z. Phys. C34 (1987), 335.
- H. Matsumoto, Prog. Theor. Phys. 79 (1988), 373[PTP].
- T. Arimitsu and H. Umezawa, Prog. Theor. Phys. 77 (1987), 53[PTP]; Prog. Theor. Phys. Suppl. No. 86 (1986), 243[PTP].
- See for example, A. C. Zaanen, Linear Analysis (North-Holland Pub., Amsterdam, 1964).
- H. Matsumoto, in Quantum Field Theory ( Proceeding of the International Symposium in honor of Hiroomi Umezawa, Positano, 1985), ed. F. Mancini (North-Holland, Amsterdam, 1986), p. 415.
- See also, F. Riesz and B. Sz. Nagy, Functional Analysis (Frederick Unger Pub. Co., New York, 1965).
N. Dunford and J. T. Schwartz, Linear Operators (Interscience Pub., New York, 1964). A compact summary which is suitable for physicists is found in M. Ida, Prog. Theor. Phys. 43 (1970), 808[PTP].
- H. Matsumoto, “Self-Consistent Perturbation Method in Thermo Field Dynamics–General Scheme–” Preprint, Univ. of Salerno, 1986.
Citing Article(s) :
Progress of Theoretical Physics Vol. 80 No. 1 (1988) pp. 57-82
Self-Consistent Perturbation Method in Thermo Field Dynamics