Critical dynamics of the phase transition to the superfluid state

Yu. A. Zhavoronkov   ; M. V. Komarova   ; Yu. G. Molotkov   ; M. Yu. Nalimov   ; J. Honkonen

Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 361-377

Résumé

In papers devoted to superfluidity, the generally accepted statement that the dynamics of the corresponding phase transition is described by the stochastic model F or E can be frequently found. Nevertheless, the dynamical critical index has not been found even in the leading order of the perturbation theory. It is also unknown which model, E or F, in fact corresponds to this system. We use two different approaches to study this problem. First, we study the dynamics of the critical behavior in a neighborhood of the $\lambda$ point using the renormalization group method based on a quantum microscopic model in the formalism of the time-dependent Green's functions at a finite temperature. Second, we study the stochastic model F to find whether it is stable under compressibility effects. Both approaches lead to the same very unexpected result: the dynamics of the phase transition to the superfluid state are described by the stochastic model A with a known dynamical critical index.

Détail

Keywords: superfluidity, stochastic dynamics, quantum field theory, quantum-field renormalization group, $(4-\epsilon)$-expansion.
Mots-clés : $\lambda$ point

Bibliographie

[1] A. N. Vasilev, Kvantovopolevaya renormgruppa v teorii kriticheskogo povedeniya i stokhasticheskoi dinamike, Izd-vo PIYaF, SPb., 1998 | DOI | MR | Zbl

[2] J. A. Lipa, J. A. Nissen, D. A. Stricker, D. R. Swanson, T. C. P. Chui, “Specific heat of liquid helium in zero gravity very near the lambda point”, Phys. Rev. B, 68:17 (2003), 174518, 25 pp., arXiv: cond-mat/0310163 | DOI

[3] P. C. Hohenberg, B. I. Halperin, “Theory of dynamic critical phenomena”, Rev. Modern Phys., 49:3 (1977), 435–479 ; R. Folk, G. Moser, “Critical dynamics: a field-theoretical approach”, J. Phys. A, 39:24 (2006), R207–R313 | DOI | DOI | MR

[4] M. Dančo, M. Hnatič, M. V. Komarova, T. Lučivjanský, M. Yu. Nalimov, “Superfluid phase transition with activated velocity fluctuations: renormalization group approach”, Phys. Rev. E, 93:1 (2016), 012109, 13 pp., arXiv: 1512.05510

[5] M. Gnatich, M. V. Komarova, M. Yu. Nalimov, “Mikroskopicheskoe obosnovanie stokhasticheskoi F-modeli kriticheskoi dinamiki”, TMF, 175:3 (2013), 398–407 | DOI | DOI | MR | Zbl

[6] C. de Dominicis, L. Peliti, “Deviations from dynamic scaling in helium and antiferromagnets”, Phys. Rev. Lett., 38:9 (1977), 505–508 | DOI

[7] C. de Dominicis, L. Peliti, “Field-theory renormalization and critical dynamics above $T_\mathrm{c}$: helium, antiferromagnets, and liquid-gas systems”, Phys. Rev. B, 18:1 (1978), 353–376 | DOI

[8] V. Dohm, “Density correlation function and dynamic transient exponents for liquid helium at and above $Y_\lambda$”, Z. Phys. B, 33:1 (1979), 79–95 | DOI

[9] L. Ts. Adzhemyan, M. Dančo, M. Hnatič, E. V. Ivanova, M. V. Kompaniets, “Multi-loop calculations of anomalous exponents in the models of critical dynamics”, EPJ Web Conf., 108 (2016), 02004, 6 pp. | DOI

[10] B. I. Halperin, P. C. Hohenberg, E. D. Siggia, Phys. Rev. B, 13:3 (1975), 1299–1328 | DOI

[11] L. Ts. Adzhemyan, S. V. Novikov, L. Sladkoff, “Raschet dinamicheskogo indeksa modeli $A$ kriticheskoi dinamiki v poryadke $\varepsilon^4$”, Vestn. S.-Peterb. un-ta. Ser. 4. Fizika. Khimiya, 4 (2008), 110–114

[12] L. Ts. Adzhemyan, S. E. Vorobeva, E. V. Ivanova, M. V. Kompaniets, “Predstavlenie renormgruppovykh funktsii nesingulyarnymi integralami v modeli kriticheskoi dinamiki ferromagnetikov: chetvertyi poryadok $\varepsilon$-razlozheniya”, TMF, 195:1 (2018), 105–116 | DOI | DOI

[13] J. Honkonen, M. V. Komarova, M. Yu. Nalimov, “Large-order asymptotes for dynamic models near equilibrium”, Nucl. Phys. B, 707:3 (2005), 493–508 | DOI | MR

[14] M. Yu. Nalimov, V. A. Sergeev, L. Sladkoff, “Borelevskoe peresummirovanie $\varepsilon$-razlozheniya dinamicheskogo indeksa $z$ modeli A $\phi^4(O(n))$-teorii”, TMF, 159:1 (2009), 96–108 | DOI | DOI | MR | Zbl

[15] L. T. Adzhemyan, E. V. Ivanova, M. V. Kompaniets, S. Y. Vorobyeva, “Diagram reduction in problem of critical dynamics of ferromagnets: 4-loop approximation”, J. Phys. A: Math. Theor., 51:15 (2018), 155003, 16 pp. | DOI | MR

[16] L. D. Landau, E. M. Lifshits, Kurs teoreticheskoi fiziki, v. VI, Gidrodinamika, Nauka, M., 1988 | MR | MR | Zbl

[17] A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinskii, Metody kvantovoi teorii polya v statisticheskoi fizike, Dobrosvet, M., 1998 | MR

[18] J. Schwinger, “Brownian motion of a quantum oscillator”, J. Math. Phys., 2:3 (1961), 407–432 | DOI | MR

[19] L. V. Keldysh, “Diagramnaya tekhnika dlya neravnovesnykh protsessov”, ZhETF, 47:4 (1965), 1515–1527 | MR

[20] Yu. Khonkonen, “Konturno uporyadochennye funktsii Grina v stokhasticheskoi teorii polya”, TMF, 175:3 (2013), 455–464 | DOI | DOI | MR | Zbl

[21] J. Honkonen, M. V. Komarova, Yu. G. Molotkov, M. Yu. Nalimov, “Effective large-scale model of boson gas from microscopic theory”, Nucl. Phys. B., 939 (2019), 105 | DOI

[22] P. C. Martin, E. D. Siggia, H. A. Rose, “Statistical dynamics of classical systems”, Phys. Rev. A, 8:1 (1973), 423–437 | DOI

[23] L. Ts. Adzhemyan, A. N. Vasilev, M. Gnatich, Yu. M. Pismak, “Kvantovo-polevaya renormgruppa v teorii stokhasticheskoi lengmyurovskoi turbulentnosti”, TMF, 78:3 (1989), 368–383 | DOI | MR

[24] U. C. Täuber, S. Diehl, “Perturbative field-theoretic renormalization group approach to driven-dissipative Bose–Einstein criticality”, Phys. Rev. X, 4 (2014), 021010, 21 pp., arXiv: 1312.5182 | DOI

[25] M. Yu. Nalimov, I. S. Nikitin, “Infrakrasnaya teoriya vozmuschenii kak metod isklyucheniya zvukovykh mod iz uravnenii stokhasticheskoi dinamiki”, Vestn. S.-Peterb. un-ta. Ser. 4. Fizika. Khimiya, 4:25 (1999), 105–109

[26] N. V. Antonov, A. N. Vasilev, “Kriticheskaya dinamika kak teoriya polya”, TMF, 60:1 (1984), 59–71 | DOI