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Prog. Theor. Phys. Vol. 54 No. 6 (1975) pp. 1679-1692

Coherent Representation of Dynamical Renormalization Group in Bose Systems

Fumihiko Tanaka

Department of Physics, University of Tokyo, Tokyo 113

(Received June 19, 1975)

Abstract:

The renormalization group transformation near four space-dimensions is extended to irreversible processes of a quantum Bose system in terms of a coherent-state formalism. Recursion relations for a kinetic equation are obtained explicitly up to O(ε²), where ε≡4-d and d denotes the space dimensionality. It is shown that terms representing the quantum effects become “irrelevant” by renormalization group scale transformation which can be carried out in the case of quantum fields due to coherent-state formalism. The complex parameter S introduced by Abrahams and Tsuneto phenomenologically is obtained from the microscopic point of view by eliminating microscopic (non-critical) fluctuations. It is also shown that S is driven to the TDGL type at the fixed point, so that the dynamical critical exponent z agrees with that obtained by Halperin, Hohenberg and Ma in the TDGL model.

URL : http://ptp.ipap.jp/link?PTP/54/1679/
DOI : 10.1143/PTP.54.1679

[ Full Text PDF : FREE ACCESS (1144K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. M. Suzuki and G. Igarashi, Phys. Lett. A 47 (1974), 361[CrossRef].
2. I. Kondor and P. Széphalusy, Phys. Lett. A 47 (1974), 393[CrossRef].
   R. Abe and S. Hikami, Phys. Lett. A 47 (1974), 341[CrossRef].
   R. Abe, Prog. Theor. Phys. 52 (1974), 1135[PTP].
   M. Suzuki and F. Tanaka, Prog. Theor. Phys. 52 (1974), 344[PTP].
   M. Suzuki, Prog. Theor. Phys. 53 (1975), 97[PTP]; Phys. Lett. A 48 (1974), 315[CrossRef].
3. K. G. Wilson and J. Kogut, Phys. Rep. 12 (1974), 75[CrossRef].
4. K. G. Wilson, Phys. Rev. Lett. 28 (1972), 548[APS].
5. M. Suzuki, Phys. Rev. Lett. 28 (1972), 507[APS]; Prog. Theor. Phys. 50 (1973), 393[PTP].
6. E. Abrahams and T. Tsuneto, Phys. Rev. B 11 (1975), 4498[APS].
   See, also Y. Yamashita and T. Tsuneto, Prog. Theor. Phys. 51 (1974), 949[PTP]; ibid. 51 (1974), 1644[PTP].
7. C. DeDominicis, E. Brezin and J. Zinn-Justin, Saclay preprint (1975).
8. F. Tanaka, Prog. Theor. Phys. 54 (1975), 289[PTP].
9. K. Kawasaki, Ann. of Phys. 61 (1970), 1[CrossRef].
   A. M. Polyakov, Sov. Phys.-JETP 30 (1970), 1164.
10. B. I. Halperin, P. C. Hohenberg and E. Siggia, Phys. Rev. Lett. 32 (1974), 1289[APS].
11. S. Ma, Phys. Rev. A 7 (1973), 2172[APS].
12. J. S. Langer, Phys. Rev. 184 (1969), 219[APS].
13. F. Tanaka, Prog. Theor. Phys. 53 (1975), 901[PTP].
14. J. S. Langer, Phys. Rev. 167 (1968), 183[APS].
15. M. Suzuki and F. Tanaka, Prog. Theor. Phys. 52 (1974), 722[PTP].
16. B. I. Halperin, P. C. Hohenberg and S. Ma, Phys. Rev. Lett. 29 (1972), 1548[APS]; Phys. Rev. B 10 (1974), 139[APS].
    See, also:
    M. Suzuki and G. Igarashi, Prog. Theor. Phys. 49 (1973), 1070[PTP].
    M. Suuki, Prog. Theor. Phys. 50 (1973), 1769[PTP]; ibid. 51 (1974), 1257[PTP].
    H. Yahata, Prog. Theor. Phys. 52 (1974), 871[PTP].
17. S. Ma and G. F. Mazenko, Phys. Rev. Lett. 33 (1974), 1384[APS]; Phys. Rev. B 11 (1975), 4077[APS].
18. Y. Kuramoto, Prog. Theor. Phys. 51 (1974), 1712[PTP].
19. F. J. Wegner and A. Houghton, Phys. Rev. A 8 (1973), 401[APS].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 58 No. 3 (1977) pp. 1045-1047 :

   Scaling Equation of State for a Bose System

   K. K. Singh

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