Abstract
We examine the effective theory of critical dynamics near superfluid phase transitions in the framework of the Keldysh-Schwinger formalism. We focus on the sector capturing the dynamics of the complex order parameter and the conserved current corresponding to the broken global symmetry. After constructing the theory up to quadratic order in the a-fields, we compare the resulting stochastic system with Model F as well as with holography. We highlight the role of a time independent gauge symmetry of the effective theory also known as “chemical shift”. Finally, we consider the limiting behaviour at energies much lower than the gap of the amplitude mode by integrating out the high energy degrees of freedom to reproduce the effective theory of superfluids.
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References
L. Van Hove, Time-dependent correlations between spins and neutron scattering in ferromagnetic crystals, Phys. Rev. 95 (1954) 1374.
L.D. Landau and I.M. Khalatnikov, On the anomalous absorption of sound near a second-order phase transition point, Dokl. Akad. Nauk SSSR 96 (1954) 626 [INSPIRE].
K. Kawasaki, Anomalous spin diffusion in ferromagnetic spin systems, J. Phys. Chem. Solids 28 (1967) 1277.
M. Fixman, Radius of gyration of polymer chains, J. Chem. Phys. 36 (1962) 306.
K. Kawasaki, Correlation-function approach to the transport coefficients near the critical point. I, Phys. Rev. 150 (1966) 291 [INSPIRE].
K. Kawasaki, Kinetic equations and time correlation functions of critical fluctuations, Ann. Phys. 61 (1970) 1.
L.P. Kadanoff and J. Swift, Transport coefficients near the liquid-gas critical point, Phys. Rev. 166 (1968) 89 [INSPIRE].
K.G. Wilson and J.B. Kogut, The renormalization group and the ε expansion, Phys. Rept. 12 (1974) 75 [INSPIRE].
P.C. Hohenberg and B.I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49 (1977) 435 [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Topological sigma models & dissipative hydrodynamics, JHEP 04 (2016) 039 [arXiv:1511.07809] [INSPIRE].
M. Crossley, P. Glorioso and H. Liu, Effective field theory of dissipative fluids, JHEP 09 (2017) 095 [arXiv:1511.03646] [INSPIRE].
R. Kubo, Statistical mechanical theory of irreversible processes. 1. General theory and simple applications in magnetic and conduction problems, J. Phys. Soc. Jap. 12 (1957) 570 [INSPIRE].
P.C. Martin and J.S. Schwinger, Theory of many particle systems. 1, Phys. Rev. 115 (1959) 1342 [INSPIRE].
X. Chen-Lin, L.V. Delacrétaz and S.A. Hartnoll, Theory of diffusive fluctuations, Phys. Rev. Lett. 122 (2019) 091602 [arXiv:1811.12540] [INSPIRE].
A. Jain and P. Kovtun, Late time correlations in hydrodynamics: beyond constitutive relations, Phys. Rev. Lett. 128 (2022) 071601 [arXiv:2009.01356] [INSPIRE].
A. Jain, P. Kovtun, A. Ritz and A. Shukla, Hydrodynamic effective field theory and the analyticity of hydrostatic correlators, JHEP 02 (2021) 200 [arXiv:2011.03691] [INSPIRE].
H. Mori, Transport, collective motion, and Brownian motion, Prog. Theor. Phys. 33 (1965) 423 [INSPIRE].
M. Lax, Fluctuations from the nonequilibrium steady state, Rev. Mod. Phys. 32 (1960) 25.
H. Liu and P. Glorioso, Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics, PoS TASI2017 (2018) 008 [arXiv:1805.09331] [INSPIRE].
S. Dubovsky, L. Hui, A. Nicolis and D.T. Son, Effective field theory for hydrodynamics: thermodynamics, and the derivative expansion, Phys. Rev. D 85 (2012) 085029 [arXiv:1107.0731] [INSPIRE].
I. Khalatnikov and V. Lebedev, Relativistic hydrodynamics of a superfluid liquid, Phys. Lett. A 91 (1982) 70.
C.P. Herzog, N. Lisker, P. Surowka and A. Yarom, Transport in holographic superfluids, JHEP 08 (2011) 052 [arXiv:1101.3330] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A theory of first order dissipative superfluid dynamics, JHEP 05 (2014) 147 [arXiv:1105.3733] [INSPIRE].
K. Damle and S. Sachdev, Nonzero-temperature transport near quantum critical points, Phys. Rev. B 56 (1997) 8714 [cond-mat/9705206] [INSPIRE].
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [INSPIRE].
A. Kapustin and L. Mrini, Universal time-dependent Ginzburg-Landau theory, Phys. Rev. B 107 (2023) 144514 [arXiv:2209.03391] [INSPIRE].
A. Donos and P. Kailidis, Nearly critical holographic superfluids, JHEP 12 (2022) 028 [Erratum ibid. 07 (2023) 232] [arXiv:2210.06513] [INSPIRE].
B.I. Halperin, P.C. Hohenberg and S.-K. Ma, Renormalization-group methods for critical dynamics: 1. Recursion relations and effects of energy conservation, Phys. Rev. B 10 (1974) 139 [INSPIRE].
A. Donos, P. Kailidis and C. Pantelidou, Dissipation in holographic superfluids, JHEP 09 (2021) 134 [arXiv:2107.03680] [INSPIRE].
Acknowledgments
We would like to thank M. Baggioli for discussions and collaboration on similar topics. We would also like to especially thank N. Iqbal for useful comments on the draft. AD is supported by STFC grant ST/T000708/1.
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Donos, A., Kailidis, P. Nearly critical superfluids in Keldysh-Schwinger formalism. J. High Energ. Phys. 2024, 110 (2024). https://doi.org/10.1007/JHEP01(2024)110
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DOI: https://doi.org/10.1007/JHEP01(2024)110