Abstract
This paper is devoted to the calculation of superfluid current in the A-phase of helium-3. This calculation is connected with the solution of a nonhomogeneous ordinary differential equation arising in the low-temperature limit from the Gor'kov equation for normal and anomalous Green functions. The new solution is obtained in the form of the expansion in the eigenfunctions of the problem of an electron in a uniform magnetic field. In the formal high-temperature limit the result obtained in the paper reproduces the known result. Bibliography: 18 titles.
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Literature Cited
R. Combescot and T. Dombre,Phys. Rev.,28B, No. 9, 5140–5149 (1983).
G. E. Volovik,Zh. Éksp. Teor. Fiz.,92, No. 6, 2116–2132 (1987)
M. C. Cross,J. Low Temp. Phys.,21, No. 5/6, 525–534 (1975).
N. D. Mermin and P. Muzikar,Phys. Rev.,21B, No. 3, 980–989 (1980).
N. B. Kopnin,Zh. Éksp. Teor. Fiz.,92, No. 6, 2106–2115 (1987).
G. E. Volovik and V. P. Mineev,Zh. Éksp. Teor. Fiz.,81, No. 3(9), 989–1000 (1981).
A. A. Abrikosov, L. P. Gor'kov, and I. E. Dzyaloshinskii,Methods of Quantum Field Theory in Statistical Physics [in Russian], Moscow (1962).
V. Alonso and V. N. Popov,Zh. Éksp. Teor. Fiz.,73, No. 4, 1445–1459 (1977).
P. N. Brusov and V. N. Popov,Superfluidity and Collective Properties of Quantum Liquids [in Russian] Moscow (1988).
N. R. Werthamer, “The Ginzburg-Landau equations and their extensions,” in:Superconductivity, Vol. 1, R. D. Parks (ed.), Marcel Dekker (1969), pp. 321–370.
R. Combescot and T. Dombre,Phys. Rev.,33B, No. 1, 79–90 (1986).
M. Abramovitz and I. A. Stegun (eds.),Handbook on Special Functions [in Russian], Moscow (1979).
P. M. Morse and H. Feshbach,Methods of Theoretical Physics [in Russian], 1, Moscow (1958).
I. S. Gradstein and I. M. Ryzhik,Tables of Integrals, Sums, Series and Products [in Russian], 4th ed., Moscow (1962).
H. Bateman and A. Erdelyi,Higher Transcendental Functions [Russian translation], Vol. 1, Moscow (1965).
P. M. Morse and H. FeshbachMethods of Theoretical Physics [Russian translation], Vol. 2, Moscow (1958).
A. V. Balatskii, G. E. Volovik, and V. A. Konyshev,Zh. Éksp. Teor. Fiz.,90, No. 6, 2038–2056 (1986).
T. Dombre and R. Combescot,Phys. Rev.,30B, No. 7, 3765–3769 (1984).
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 179–193.
Translated by K. Malyshev.
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Malyshev, K. On the two methods of calculation of the superfluid current in the A-phase of helium-3. J Math Sci 83, 113–122 (1997). https://doi.org/10.1007/BF02398466
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DOI: https://doi.org/10.1007/BF02398466