Prog. Theor. Phys. Vol. 56 No. 6 (1976) pp. 1674-1688

[ Full Text PDF : FREE ACCESS (1138K) ]

The Thomas-Kuhn Sum Rule and Superfluidity. I

— Applicability of Linear Response Theory to Macroscopic Systems —

Takeo Izuyama

Institute of Physics, College of General Education, University of Tokyo, Komaba, Tokyo 153

(Received June 28, 1976)

Abstract:

The linear response theory (on the linear relation between a weak external field and the response) takes into account only the linear term of the field in dealing with dynamics. In this sense the theory describes microscopic linearity. We want to apply the theory to macroscopic responses to weak macroscopic fields. The assertion of this series of papers is that we may safely do so when randomness exists in the system under consideration.
A large cyclic system under uniform external field is considered. The Kubo response current is shown to be divided into the persistent current and the Ohmic one. We are concerned with the superfluid part here. The logical gap between microscopic and macroscopic linearities is exemplified. To see how the randomness restores the gap, we analyze a few examples. We find also that neither ODLRO nor the Bose-Einstein condensation can be a sufficient condition for superfluidity.

URL : http://ptp.ipap.jp/link?PTP/56/1674/
DOI : 10.1143/PTP.56.1674

References:

R. Kubo, J. Phys. Soc. Jpn. 12 (1957), 570[JPSJ].
P. C. Martin and J. Schwinger, Phys. Rev. 115 (1959), 1342[APS].
H. Nakano, Prog. Theor. Phys. 15 (1956), 77[PTP].
S. Nakajima, Proc. Phys. Soc. A 69 (1956), 441.
N. G. van Kampen, Physica Norvegica 5 (1971), 279.
W. Thomas, Naturwiss. 13 (1925), 627.
W. Kuhn, Z. Phys. 33 (1925), 408.
C. N. Yang, Rev. Mod. Phys. 34 (1962), 694[APS].
T. Izuyama, Phys. Rev. B 5 (1972), 190[APS].
T. Izuyama, Prog. Theor. Phys. 48 (1972), 1106[PTP].
T. Izuyama, Prog. Theor. Phys. 50 (1973), 1265[PTP].
T. Izuyama, Prog. Theor. Phys. 50 (1973), 841[PTP].
D. A. Greenwood, Proc. Phys. Soc. 71 (1958), 585.
P. W. Anderson, Phys. Rev. 109 (1958), 1492[APS].
R. E. Borland, Proc. Phys. Soc. 78 (1961), 926.
W. Kohn, Phys. Rev. 133 (1964), A171[APS].
W. Kohn and D. Sherrington, Rev. Mod. Phys. 42 (1970), 1[APS].
J. M. Luttinger and H. K. Sy, Phys. Rev. A 7 (1973), 712[APS].
S. Moriguchi, K. Udagawa and S. Ichimatsu, Mathematical Formulae III (Iwanami Co. Ltd., 1967), p. 26 (in Japanese).

Citing Article(s) :

Progress of Theoretical Physics Vol. 57 No. 1 (1977) pp. 42-53 :
The Thomas-Kuhn Sum Rule and Superfluidity. II

Takeo Izuyama