A theoretical description of the new phases of liquid <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi mathvariant="normal">He</mi></mrow><mprescripts></mprescripts><mrow></mrow><mrow><mn>3</mn></mrow><mrow></mrow><mrow></mrow></mmultiscripts></mrow></math></span>

Anthony J. Leggett

doi:10.1103/RevModPhys.47.331

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A theoretical description of the new phases of liquid ${}^{3}{He}$

Anthony J. Leggett

School of Mathematical and Physical Sciences, University of Sussex, Falmer Brighton, England

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Rev. Mod. Phys. 47, 331 – Published 1 April, 1975Erratum Rev. Mod. Phys. 48, 357 (1976)

DOI: https://doi.org/10.1103/RevModPhys.47.331

Abstract

This paper reviews the theory of anisotropic superfluid phases and its application to the new A and B phases of liquid ${}^{3}{He}$ . It is tutorial in nature and advanced formal techniques are avoided; even the formalism of second quantization is not required. After an initial discussion of the Fermi-liquid theory of Landau and its application to the normal phase of liquid ${}^{3}{He}$ , the idea of instability against formation of Cooper pairs is introduced. The effective interaction in liquid ${}^{3}{He}$ is considered, with emphasis on the spin-dependent interaction arising from virtual spin polarization of the medium ("spin fluctuation exchange"). Next, a self-contained discussion of the "weak-coupling" BCS theory as applied to anisotropic superfluids is given, with special attention to the "Ginzburg-Landau" region close to the transition temperature. Formulas are derived for the specific heat, spin susceptibility, normal density tensor, and static spin-dependent correlation properties of superfluids with both singlet and triplet pairing: In the triplet case the ideas of "spin superfluid velocity" and "spin superfluid density" are also introduced. After a preliminary comparison of the weak-coupling theory with experiment, it is shown that feedback effects due to the modification, by formation of Cooper pairs, of the effective interaction connected with spin fluctuation exchange can produce results which are qualitatively different from those of the weak-coupling theory. An attempt is made to reformulate recent graph-theoretical treatments of this phenomenon in a more elementary language, and considerations based on possible invariant forms of the free energy are also introduced. The properties of the so-called Anderson-Brinkman-Morel and Balian-Werthamer states, which are commonly identified with ${}^{3}{He}$ -A and B, respectively, are studied in detail. Next, the effects which tend to orient the Cooper pair wave function in a given experimental situation are discussed; in this context the form of the free energy terms arising from spatial variation of the wave function is explored. A semiphenomenological theory of the nuclear magnetic resonance properties is developed and applied in particular to the case of unsaturated cw resonance; the analogy with the Josephson effect is emphasized. The question of relaxation and linewidths is also briefly discussed. A partial account is given of the theory of finite-wavelength collective oscillations, with particular reference to first, second, and fourth sound and spin waves. The splitting of the A-normal transition in a magnetic field is considered, with special attention to the possibility it offers of testing theories of the "spin fluctuation" type. Finally, a brief assessment is made of the extent to which the current experimental data support the conventional identification of ${}^{3}{He}$ -A and B and the spin fluctuation theory, and some outstanding problems and possibilities are outlined. Subjects not discussed include "first-principles" theories of the effective interaction in ${}^{3}{He}$ collective excitations in the "collisionless" regime, and the problem of ultrasonic absorption, "orbit waves," and the theory of the kinetic coefficients.

Erratum

Erratum: A theoretical description of the new phases of liquid ${}^{3}{He}$

A. J. Leggett

Rev. Mod. Phys. 48, 357 (1976)

References (120)

Abrikosov, A. A. and I. M. Khalatnikov, 1959, Rep. Prog. Phys. 22, 329
Ahonen, A. I., M. T. Haikala, M. Krusius, and O. V. Lounasmaa, 1974, Phys. Rev. Lett. 33, 628
Ambegaokar, V., 1969, Superconductivity, edited by R. D. Parks (Dekker, New York), p. 259
Ambegaokar, V., 1974, Proc. Canadian Summer School, unpublished
Omitted endnote
Ambegaokar, V., P. G. De Gennes, and D. Rainer, 1974, Phys. Rev. A 9, 2676
Ambegaokar, V. and N. D. Mermin, 1973, Phys. Rev. Lett. 30, 81
Anderson, P. W., 1958, Phys. Rev. 112, 1900
Anderson, P. W., 1973, Phys. Rev. Lett. 30, 368
Anderson, P. W. and W. F. Brinkman, 1973, Phys. Rev. Lett. 30, 1108
Anderson, P. W. and P. Morel, 1961, Phys. Rev. 123, 1911
Anderson, P. W. and C. M. Varma, 1973, Nature (Lond.) 241, 187
Balian, R. and N. R. Werthamer, 1963, Phys. Rev. 131, 1553
Bardeen, J., L. N. Cooper, and J. R. Schrieffer, 1957, Phys. Rev. 108, 1175
Barton, G. and M. A. Moore, 1973, unpublished
Barton, G. and M. A. Moore, 1974a, J. Phys. C. 7, 2989
Barton, G. and M. A. Moore, 1974b, J. Phys. C. 8 (in press)
Barton, G. and M. A. Moore, 1974c (to be published)
Baym, G. and C. Pethick, 1974, "Landau Fermi Liquid Theory and Low Temperature Properties of Liquid ${}^{3}{He}$ " (to be published)
Berk, N. F. and J. R. Schrieffer, 1966, Phys. Rev. Lett. 17, 433
Betbeder-Matibet, O. and P. Nozieres, 1969, Ann. Phys. (New York) 51, 932
Bogoliubov, N. N., 1958, Zh. Eksp. Teor. Fiz. 34, 735
Brinkman, W. F., 1974, Phys. Lett. 49, A, 411
Brinkman, W. F. and P. W. Anderson, 1973, Phys. Rev. A 8, 2732
Brinkman, W. F., J. Serene, and P. W. Anderson, 1974, Phys. Rev. A 10, 2386
Brinkman, W. F. and H. Smith, 1974, Phys. Rev. A 10, 2325
Brinkman, W. F., H. Smith, D. D. Osheroff, and E. I. Blount, 1974, Phys. Rev. Lett. 33, 624
Combescot, R., 1974a, Phys. Rev. A 10, 1700
Combescot, R., 1974b, Phys. Rev. Lett. 33, 946
Combescot, R. and H. Ebisawa, 1974, Phys. Rev. Lett. 33, 810
Cooper, L. N., 1956, Phys. Rev. 104, 1189
Corruccini, L. R., D. D. Osheroff, D. M. Lee, and R. C. Richardson, Phys. Rev. Lett. 27, 650
Czerwonko, J., 1967, Acta Phys. Pol. 32, 335
De Gennes, P. G., 1966, Superconductivity of Metals and Alloys (Benjamin, New York)
De Gennes, P. G., 1973a, Phys. Lett. A 44, 271
De Gennes, P. G., 1973b, Proc. 24th Nobel Symposium, Aspenasgarden, Sweden, edited by B. Lundqvist and S. Lundqvist (Academic, New York), p. 112
De Gennes, P. G. and D. Rainer, 1974, Phys. Lett. A 46, 429
Delrieu, J. M., 1974, J. de Physique Lett. 35, L-189 Erratum, ibid. 36, L-22 (1975)
De Shalit, A. and I. Talmi, 1963, Nuclear Shell Theory (Academic, New York)
Ebisawa, H. and K. Maki, 1974, Prog. Theor. Phys. (Kyoto) 51, 337
Engelsberg, S., W. F. Brinkman, and P. W. Anderson, 1974, Phys. Rev. A 9, 2592
Fujita, T. and T. Tsuneto, 1974 (to be published)
Ginzburg, V. L. and L. D. Landau, 1950, Zh. Eksperim. Teor. Fiz. 20, 1064
Glassgold, A. E. and A. M. Sessler, 1961, Nuovo Cimento 19, 723
Graham, R., 1974, Phys. Rev. Lett. 33, 1431
Galasiewicz, Z. M., 1974, Phys. Cond. Matter 18, 141
Josephson, B. D., 1969, in Superconductivity, edited by R. D. Parks (Dekker, New York), p. 423
Khalatnikov, I. M., 1965, Introduction to the Theory of Superfluidity (Benjamin, New York)
Kibble, T. W. B, 1966, Classical Mechanics (McGraw-Hill, London)
Kuroda, Y., 1974a, Prog. Theor. Phys. (Kyoto) 51, 1269
Kuroda, Y., 1974b (to be published)
Landau, L. D., 1957, Zh. Eksperim Teor. Fiz. 32, 59
Landau, L. D. and Lifshitz, E. M., 1965, Quantum Mechanics (Pergamon, London). p. 111
Langer, J. M. and M. E. Fisher, 1967, Phys. Rev. Lett. 19, 560
Layzer, A. and D. Fay, 1971, Int. J. Mag. 1, 135
Layzer, A. and D. Fay, 1974a, Solid State Commun. 15, 599
Layzer, A. and D. Fay, 1974b, Proc. EPS Topical Conference on Liquid and Solid Helium, Haifa (to be published)
Leggett, A. J., 1965, Phys. Rev. 140, A 1869
Leggett, A. J., 1968, Ann. Phys. (New York) 46, 76
Leggett, A. J., 1970, J. Phys. C 12, 447
Leggett, A. J., 1972, Phys. Rev. Lett. 29, 1227
Leggett, A. J. 1973a, Phys. Rev. Lett. 31, 352
Leggett, A. J., 1973b, J. Phys. C 6, 3187
Leggett, A. J., 1974a, Ann. Phys. (New York) 85, 11
Leggett, A. J., 1974b, Prog. Theor. Phys. (Kyoto) 51, 1275
Leggett, A. J. and M. J. Rice, 1968, Phys. Rev. Lett. 20, 586
Lindhard, J., 1954, K. Dan. Vidensk. Selsk., Mat.-Fys. Medd. 28, 8
Maki, K., 1974a (to be published)
Maki, K., 1974b, J. Low Temp. Phys. 16, 465
Maki, K. and H. Ebisawa, 1973, Prog. Theor. Phys. (Kyoto) 50, 1452
Maki, K. and H. Ebisawa, 1974a, J. Low Temperature Phys. 15, 213
Maki, K. and H. Ebisawa, 1974b, Prog. Theor. Phys. (Kyoto) 51, 690
Maki, K. and H. Ebisawa, 1974c, Phys. Rev. Lett. 32, 520
Maki, K. and C. R. Hu, 1974 (to be published)
Maki, K. and T. Tsuneto, 1974a, Prog. Theor. Phys. 52 (to be published)
Maki, K. and T. Tsuneto, 1974b, Prog. Theor. Phys. (Kyoto) 52, 773
Mercereau, J. E., 1969, in Superconductivity, edited by R. D. Parks (Dekker, New York), p. 393
Mermin, N. D., 1974, Phys. Rev. A 9, 868
Mermin, N. D. and V. Ambegaokar, 1973, Proc. 24th Nobel Symposium, Aspenasgarden, Sweden, edited by B. Lundqvist and S. Lundqvist (Academic, New York), p. 97
Mermin, N. D. and G. Stare, 1973, Phys. Rev. Lett. 30, 1135
Mermin, N. D. and G. Stare, 1974 (to be published)
Messiah, A., 1966, Quantum Mechanics (North-Holland, Amsterdam), Vol. I
Moore, M. A., M. Vuorio, T. Haavasoja, H. J. Vidberg, 1974, J. Phys. C 7, L418
Morel, P. and P. Nozières, 1962, Phys. Rev. 126, 1909
Nakajima, S., 1973, Prog. Theor. Phys. (Kyoto) 50, 1101
Nozières, P., 1964, Theory of Interacting Fermi Systems (Benjamin, New York)
Osheroff, D. D., 1973, thesis, Cornell University (unpublished)
Osheroff, D. D., 1974, Phys. Rev. Lett. 33, 1009
Osheroff, D. D. and P. W. Anderson, 1974, Phys. Rev. Lett. 33, 686
Osheroff, D. D. and W. F. Brinkman, 1974, Phys. Rev. Lett. 32, 584
Østgaard, E., 1969, Phys. Rev. 187, 371
Østgaard, E., 1974, Phys. Lett. A 49, 433
Patton, B. R., 1974, Phys. Lett. A 47, 391
Pines, D. and P. Nozières, 1966, The Theory of Quantum Liquids (Benjamin, New York), Vol. I
Privorotskii, I. M., 1974 (to be published)
Putterman, S. J., 1973, Phys. Rev. Lett. 30, 1165
Rickayzen, G., 1965, Theory of Superconductivity (Interscience, New York)
Saslow, W. M., 1973, Phys. Rev. Lett. 31, 870
Seiden, J., 1973, C. R. Acad. Sci. (Paris) B 276, 905
Serene, J., 1973, thesis, Cornell University (unpublished)
Shahzamanian, M. A., 1974 (to be published)
Shumeiko, V. S., 1972, Zh. Eksperim. Teor. Fiz. 63, 621 [English translation: Sov. Phys.—JETP 36, 330 (1972)]
Soda, T. and K. Fujiki, 1974 (to be published)
Takagi, S., 1973, thesis, University of Tokyo (unpublished)
Takagi, S., 1974a Prog. Theor. Phys. (Kyoto) 51, 674
Takagi, S., 1974b, J. Low Temp. Phys. 18, 309
Takagi, S., 1974c (to be published)
Takagi, S., 1974d, Prog. Theor. Phys. (Kyoto) 51, 635
Takagi, S., 1974e, Prog. Theor. Phys. (Kyoto) 51, 1998
Tewordt, L., 1974a, J. Low Temp. Phys. 15, 349
Tewordt, L., 1974b, Z. Phys. 268, 207
Tewordt, L., D. Fay, P. Dörre, D. Einzel, 1974 (to be published)
Thouless, D., 1960, Ann. Phys. (New York) 10, 553
Vuorio, M., 1974, J. Phys. C 7, L5
Wheatley, J. C., 1975, Rev. Mod. Phys., this issue
Wölfle, P., 1973a, Phys. Rev. Lett. 30, 1169
Wölfle, P., 1973b, Phys. Rev. Lett. 31, 1437
Wölfle, P., 1974a, Phys. Lett. A 47, 224
Wölfle, P., 1974b, J. Low Temp. Phys. (to be published)
Yosida, K., 1958, Phys. Rev. 110, 769

[c1] Abrikosov, A. A. and I. M. Khalatnikov, 1959, Rep. Prog. Phys. 22, 329

[c2] Ahonen, A. I., M. T. Haikala, M. Krusius, and O. V. Lounasmaa, 1974, Phys. Rev. Lett. 33, 628

[c3] Ambegaokar, V., 1969, Superconductivity, edited by R. D. Parks (Dekker, New York), p. 259

[c4] Ambegaokar, V., 1974, Proc. Canadian Summer School, unpublished

[c5] Omitted endnote

[c6] Ambegaokar, V., P. G. De Gennes, and D. Rainer, 1974, Phys. Rev. A 9, 2676

[c7] Ambegaokar, V. and N. D. Mermin, 1973, Phys. Rev. Lett. 30, 81

[c8] Anderson, P. W., 1958, Phys. Rev. 112, 1900

[c9] Anderson, P. W., 1973, Phys. Rev. Lett. 30, 368

[c10] Anderson, P. W. and W. F. Brinkman, 1973, Phys. Rev. Lett. 30, 1108

[c11] Anderson, P. W. and P. Morel, 1961, Phys. Rev. 123, 1911

[c12] Anderson, P. W. and C. M. Varma, 1973, Nature (Lond.) 241, 187

[c13] Balian, R. and N. R. Werthamer, 1963, Phys. Rev. 131, 1553

[c14] Bardeen, J., L. N. Cooper, and J. R. Schrieffer, 1957, Phys. Rev. 108, 1175

[c15] Barton, G. and M. A. Moore, 1973, unpublished

[c16] Barton, G. and M. A. Moore, 1974a, J. Phys. C. 7, 2989

[c17] Barton, G. and M. A. Moore, 1974b, J. Phys. C. 8 (in press)

[c18] Barton, G. and M. A. Moore, 1974c (to be published)

[c19] Baym, G. and C. Pethick, 1974, "Landau Fermi Liquid Theory and Low Temperature Properties of Liquid ${}^{3}{He}$ " (to be published)

[c20] Berk, N. F. and J. R. Schrieffer, 1966, Phys. Rev. Lett. 17, 433

[c21] Betbeder-Matibet, O. and P. Nozieres, 1969, Ann. Phys. (New York) 51, 932

[c22] Bogoliubov, N. N., 1958, Zh. Eksp. Teor. Fiz. 34, 735

[c23] Brinkman, W. F., 1974, Phys. Lett. 49, A, 411

[c24] Brinkman, W. F. and P. W. Anderson, 1973, Phys. Rev. A 8, 2732

[c25] Brinkman, W. F., J. Serene, and P. W. Anderson, 1974, Phys. Rev. A 10, 2386

[c26] Brinkman, W. F. and H. Smith, 1974, Phys. Rev. A 10, 2325

[c27] Brinkman, W. F., H. Smith, D. D. Osheroff, and E. I. Blount, 1974, Phys. Rev. Lett. 33, 624

[c28] Combescot, R., 1974a, Phys. Rev. A 10, 1700

[c29] Combescot, R., 1974b, Phys. Rev. Lett. 33, 946

[c30] Combescot, R. and H. Ebisawa, 1974, Phys. Rev. Lett. 33, 810

[c31] Cooper, L. N., 1956, Phys. Rev. 104, 1189

[c32] Corruccini, L. R., D. D. Osheroff, D. M. Lee, and R. C. Richardson, Phys. Rev. Lett. 27, 650

[c33] Czerwonko, J., 1967, Acta Phys. Pol. 32, 335

[c34] De Gennes, P. G., 1966, Superconductivity of Metals and Alloys (Benjamin, New York)

[c35] De Gennes, P. G., 1973a, Phys. Lett. A 44, 271

[c36] De Gennes, P. G., 1973b, Proc. 24th Nobel Symposium, Aspenasgarden, Sweden, edited by B. Lundqvist and S. Lundqvist (Academic, New York), p. 112

[c37] De Gennes, P. G. and D. Rainer, 1974, Phys. Lett. A 46, 429

[c38] Delrieu, J. M., 1974, J. de Physique Lett. 35, L-189 Erratum, ibid. 36, L-22 (1975)

[c39] De Shalit, A. and I. Talmi, 1963, Nuclear Shell Theory (Academic, New York)

[c40] Ebisawa, H. and K. Maki, 1974, Prog. Theor. Phys. (Kyoto) 51, 337

[c41] Engelsberg, S., W. F. Brinkman, and P. W. Anderson, 1974, Phys. Rev. A 9, 2592

[c42] Fujita, T. and T. Tsuneto, 1974 (to be published)

[c43] Ginzburg, V. L. and L. D. Landau, 1950, Zh. Eksperim. Teor. Fiz. 20, 1064

[c44] Glassgold, A. E. and A. M. Sessler, 1961, Nuovo Cimento 19, 723

[c45] Graham, R., 1974, Phys. Rev. Lett. 33, 1431

[c46] Galasiewicz, Z. M., 1974, Phys. Cond. Matter 18, 141

[c47] Josephson, B. D., 1969, in Superconductivity, edited by R. D. Parks (Dekker, New York), p. 423

[c48] Khalatnikov, I. M., 1965, Introduction to the Theory of Superfluidity (Benjamin, New York)

[c49] Kibble, T. W. B, 1966, Classical Mechanics (McGraw-Hill, London)

[c50] Kuroda, Y., 1974a, Prog. Theor. Phys. (Kyoto) 51, 1269

[c51] Kuroda, Y., 1974b (to be published)

[c52] Landau, L. D., 1957, Zh. Eksperim Teor. Fiz. 32, 59

[c53] Landau, L. D. and Lifshitz, E. M., 1965, Quantum Mechanics (Pergamon, London). p. 111

[c54] Langer, J. M. and M. E. Fisher, 1967, Phys. Rev. Lett. 19, 560

[c55] Layzer, A. and D. Fay, 1971, Int. J. Mag. 1, 135

[c56] Layzer, A. and D. Fay, 1974a, Solid State Commun. 15, 599

[c57] Layzer, A. and D. Fay, 1974b, Proc. EPS Topical Conference on Liquid and Solid Helium, Haifa (to be published)

[c58] Leggett, A. J., 1965, Phys. Rev. 140, A 1869

[c59] Leggett, A. J., 1968, Ann. Phys. (New York) 46, 76

[c60] Leggett, A. J., 1970, J. Phys. C 12, 447

[c61] Leggett, A. J., 1972, Phys. Rev. Lett. 29, 1227

[c62] Leggett, A. J. 1973a, Phys. Rev. Lett. 31, 352

[c63] Leggett, A. J., 1973b, J. Phys. C 6, 3187

[c64] Leggett, A. J., 1974a, Ann. Phys. (New York) 85, 11

[c65] Leggett, A. J., 1974b, Prog. Theor. Phys. (Kyoto) 51, 1275

[c66] Leggett, A. J. and M. J. Rice, 1968, Phys. Rev. Lett. 20, 586

[c67] Lindhard, J., 1954, K. Dan. Vidensk. Selsk., Mat.-Fys. Medd. 28, 8

[c68] Maki, K., 1974a (to be published)

[c69] Maki, K., 1974b, J. Low Temp. Phys. 16, 465

[c70] Maki, K. and H. Ebisawa, 1973, Prog. Theor. Phys. (Kyoto) 50, 1452

[c71] Maki, K. and H. Ebisawa, 1974a, J. Low Temperature Phys. 15, 213

[c72] Maki, K. and H. Ebisawa, 1974b, Prog. Theor. Phys. (Kyoto) 51, 690

[c73] Maki, K. and H. Ebisawa, 1974c, Phys. Rev. Lett. 32, 520

[c74] Maki, K. and C. R. Hu, 1974 (to be published)

[c75] Maki, K. and T. Tsuneto, 1974a, Prog. Theor. Phys. 52 (to be published)

[c76] Maki, K. and T. Tsuneto, 1974b, Prog. Theor. Phys. (Kyoto) 52, 773

[c77] Mercereau, J. E., 1969, in Superconductivity, edited by R. D. Parks (Dekker, New York), p. 393

[c78] Mermin, N. D., 1974, Phys. Rev. A 9, 868

[c79] Mermin, N. D. and V. Ambegaokar, 1973, Proc. 24th Nobel Symposium, Aspenasgarden, Sweden, edited by B. Lundqvist and S. Lundqvist (Academic, New York), p. 97

[c80] Mermin, N. D. and G. Stare, 1973, Phys. Rev. Lett. 30, 1135

[c81] Mermin, N. D. and G. Stare, 1974 (to be published)

[c82] Messiah, A., 1966, Quantum Mechanics (North-Holland, Amsterdam), Vol. I

[c83] Moore, M. A., M. Vuorio, T. Haavasoja, H. J. Vidberg, 1974, J. Phys. C 7, L418

[c84] Morel, P. and P. Nozières, 1962, Phys. Rev. 126, 1909

[c85] Nakajima, S., 1973, Prog. Theor. Phys. (Kyoto) 50, 1101

[c86] Nozières, P., 1964, Theory of Interacting Fermi Systems (Benjamin, New York)

[c87] Osheroff, D. D., 1973, thesis, Cornell University (unpublished)

[c88] Osheroff, D. D., 1974, Phys. Rev. Lett. 33, 1009

[c89] Osheroff, D. D. and P. W. Anderson, 1974, Phys. Rev. Lett. 33, 686

[c90] Osheroff, D. D. and W. F. Brinkman, 1974, Phys. Rev. Lett. 32, 584

[c91] Østgaard, E., 1969, Phys. Rev. 187, 371

[c92] Østgaard, E., 1974, Phys. Lett. A 49, 433

[c93] Patton, B. R., 1974, Phys. Lett. A 47, 391

[c94] Pines, D. and P. Nozières, 1966, The Theory of Quantum Liquids (Benjamin, New York), Vol. I

[c95] Privorotskii, I. M., 1974 (to be published)

[c96] Putterman, S. J., 1973, Phys. Rev. Lett. 30, 1165

[c97] Rickayzen, G., 1965, Theory of Superconductivity (Interscience, New York)

[c98] Saslow, W. M., 1973, Phys. Rev. Lett. 31, 870

[c99] Seiden, J., 1973, C. R. Acad. Sci. (Paris) B 276, 905

[c100] Serene, J., 1973, thesis, Cornell University (unpublished)

[c101] Shahzamanian, M. A., 1974 (to be published)

[c102] Shumeiko, V. S., 1972, Zh. Eksperim. Teor. Fiz. 63, 621 [English translation: Sov. Phys.—JETP 36, 330 (1972)]

[c103] Soda, T. and K. Fujiki, 1974 (to be published)

[c104] Takagi, S., 1973, thesis, University of Tokyo (unpublished)

[c105] Takagi, S., 1974a Prog. Theor. Phys. (Kyoto) 51, 674

[c106] Takagi, S., 1974b, J. Low Temp. Phys. 18, 309

[c107] Takagi, S., 1974c (to be published)

[c108] Takagi, S., 1974d, Prog. Theor. Phys. (Kyoto) 51, 635

[c109] Takagi, S., 1974e, Prog. Theor. Phys. (Kyoto) 51, 1998

[c110] Tewordt, L., 1974a, J. Low Temp. Phys. 15, 349

[c111] Tewordt, L., 1974b, Z. Phys. 268, 207

[c112] Tewordt, L., D. Fay, P. Dörre, D. Einzel, 1974 (to be published)

[c113] Thouless, D., 1960, Ann. Phys. (New York) 10, 553

[c114] Vuorio, M., 1974, J. Phys. C 7, L5

[c115] Wheatley, J. C., 1975, Rev. Mod. Phys., this issue

[c116] Wölfle, P., 1973a, Phys. Rev. Lett. 30, 1169

[c117] Wölfle, P., 1973b, Phys. Rev. Lett. 31, 1437

[c118] Wölfle, P., 1974a, Phys. Lett. A 47, 224

[c119] Wölfle, P., 1974b, J. Low Temp. Phys. (to be published)

[c120] Yosida, K., 1958, Phys. Rev. 110, 769

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A theoretical description of the new phases of liquid ${}^{3}{He}$

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Erratum: A theoretical description of the new phases of liquid ${}^{3}{He}$

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A theoretical description of the new phases of liquid He3

Abstract

Erratum

Erratum: A theoretical description of the new phases of liquid He3

References (120)

A theoretical description of the new phases of liquid ${}^{3}{He}$

Erratum: A theoretical description of the new phases of liquid ${}^{3}{He}$