Prog. Theor. Phys. Vol. 77 No. 2 (1987) pp. 262-277

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A Generalized Equation of Motion for the Linear Response. III

— Simple Application to a Quantal Spin —

Mizuhiko Saeki

Toyama Mercantile Marine College, Ebie Neriya, Shinminato, Toyama 933-02

(Received July 17, 1986)

Abstract:

The time-convolutionless equation of motion for the linear response derived in a previous paper is applied to a simple system of a quantal spin interacting weakly with its surroundings (heat bath). The operator form of equation is derived and is transcribed into the c-number one by the generalized phase-space method for spin operators. The equations of motion for the longitudinal and transverse expectation values of the spin are derived and are solved for the case of S=1/2 (S: the magnitude of spin). The longitudinal and transverse susceptibilities are derived from the stationary solutions, and are compared with the ones derived by the method of spin relaxation theory and Kubo theory for the linear response.

URL : http://ptp.ipap.jp/link?PTP/77/262/
DOI : 10.1143/PTP.77.262

References:

R. Kubo, J. Phys. Soc. Jpn. 12 (1957), 570[JPSJ].
F. Shibata, J. Phys. Soc. Jpn. 49 (1980), 15[JPSJ].
M. Asou and F. Shibata, J. Phys. Soc. Jpn. 50 (1981), 1846[JPSJ].
M. Asou and F. Shibata, J. Phys. Soc. Jpn. 50 (1981), 2481[JPSJ].
Y. Hamano and F. Shibata, J. Phys. Soc. Jpn. 51 (1982), 1727[JPSJ].
M. Saeki, Prog. Theor. Phys. 67 (1982), 1313[PTP].
M. Saeki, Prog. Theor. Phys. 73 (1985), 615[PTP].
N. Hashitsume, F. Shibata and M. Shingu, J. Stat. Phys. 17 (1977), 155.
R. Kubo, in Tokei Butsurigaku, Statistical Physics, eds. M. Toda and R. Kubo (Iwanami, Tokyo, 1978), 2nd ed., chap. 6 [in Japanese].
P. N. Argyres and P. L. Kelley, Phys. Rev. 134 (1964), A98[APS].
Y. Takahashi and F. Shibata, J. Phys. Soc. Jpn. 38 (1975), 656[JPSJ].
Y. Takahashi and F. Shibata, J. Stat. Phys. 14 (1976), 49.
M. Saeki, J. Phys. Soc. Jpn. 55 (1986), 1846[JPSJ].
R. Kubo and T. Toyabe, in Proc. of the XIV-th Colloque Ampere, Ljubljana, 1966, Magnetic Resonance and Relaxation, ed. R. Blinc (North-Holland, Amsterdam, 1967), p. 810.
F. Shibata and I. Sato, to be published in Physica A.
F. Shibata and T. Arimitsu, J. Phys. Soc. Jpn. 49 (1980), 891[JPSJ].

Citing Article(s) :

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Transverse Susceptibilities of a Quantal Spin (S=1/2)

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A Quantum Field Theoretical Approach to the TCLE Method

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Progress of Theoretical Physics Vol. 121 No. 1 (2009) pp. 165-191 :
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