Abstract
We investigate the phenomenon of second sound in various states of matter from the perspective of non-equilibrium effective field theory (EFT). In particular, for each state of matter considered, we find that at least two (though sometimes multiple) qualitatively different EFTs exist at finite temperature such that there is always at least one EFT with a propagating second-sound wave and at least one with no such second-sound wave. To aid in the construction of these EFTs, we use the method of cosets developed for non-equilibrium systems. It turns out that the difference between the EFTs with and without second-sound modes can be understood as arising from different choices of a new kind of inverse Higgs constraint. Finally, we demonstrate that it is possible to bypass the need for new inverse Higgs constraints by formulating EFTs on a new kind of manifold that is like the usual fluid worldvolume, but with reduced gauge symmetries.
References
H. Liu and P. Glorioso, Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics, PoS TASI2017 (2018) 008 [arXiv:1805.09331] [INSPIRE].
P. Glorioso, M. Crossley and H. Liu, Effective field theory of dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current, JHEP 09 (2017) 096 [arXiv:1701.07817] [INSPIRE].
M. Crossley, P. Glorioso and H. Liu, Effective field theory of dissipative fluids, JHEP 09 (2017) 095 [arXiv:1511.03646] [INSPIRE].
P. Glorioso, H. Liu and S. Rajagopal, Global Anomalies, Discrete Symmetries and Hydrodynamic Effective Actions, JHEP 01 (2019) 043 [arXiv:1710.03768] [INSPIRE].
P. Gao, P. Glorioso and H. Liu, Ghostbusters: Unitarity and Causality of Non-equilibrium Effective Field Theories, JHEP 03 (2020) 040 [arXiv:1803.10778] [INSPIRE].
P. Glorioso and H. Liu, The second law of thermodynamics from symmetry and unitarity, arXiv:1612.07705 [INSPIRE].
M. Blake, H. Lee and H. Liu, A quantum hydrodynamical description for scrambling and many-body chaos, JHEP 10 (2018) 127 [arXiv:1801.00010] [INSPIRE].
M.J. Landry, The coset construction for non-equilibrium systems, JHEP 07 (2020) 200 [arXiv:1912.12301] [INSPIRE].
M.J. Landry, Dynamical chemistry: non-equilibrium effective actions for reactive fluids, arXiv:2006.13220 [INSPIRE].
M. Baggioli and M. Landry, Effective Field Theory for Quasicrystals and Phasons Dynamics, SciPost Phys. 9 (2020) 062 [arXiv:2008.05339] [INSPIRE].
P. Romatschke and U. Romatschke, Relativistic Fluid Dynamics In and Out of Equilibrium, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2019), [DOI] [arXiv:1712.05815] [INSPIRE].
M. Harder, P. Kovtun and A. Ritz, On thermal fluctuations and the generating functional in relativistic hydrodynamics, JHEP 07 (2015) 025 [arXiv:1502.03076] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
P. Kovtun, G.D. Moore and P. Romatschke, Towards an effective action for relativistic dissipative hydrodynamics, JHEP 07 (2014) 123 [arXiv:1405.3967] [INSPIRE].
S. Grozdanov and J. Polonyi, Viscosity and dissipative hydrodynamics from effective field theory, Phys. Rev. D 91 (2015) 105031 [arXiv:1305.3670] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Two roads to hydrodynamic effective actions: a comparison, arXiv:1701.07896 [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Effective Action for Relativistic Hydrodynamics: Fluctuations, Dissipation and Entropy Inflow, JHEP 10 (2018) 194 [arXiv:1803.11155] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, The Fluid Manifesto: Emergent symmetries, hydrodynamics and black holes, JHEP 01 (2016) 184 [arXiv:1510.02494] [INSPIRE].
K. Jensen, N. Pinzani-Fokeeva and A. Yarom, Dissipative hydrodynamics in superspace, JHEP 09 (2018) 127 [arXiv:1701.07436] [INSPIRE].
K. Jensen, R. Marjieh, N. Pinzani-Fokeeva and A. Yarom, A panoply of Schwinger-Keldysh transport, SciPost Phys. 5 (2018) 053 [arXiv:1804.04654] [INSPIRE].
M. Hongo, S. Kim, T. Noumi and A. Ota, Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems, Phys. Rev. D 103 (2021) 056020 [arXiv:1907.08609] [INSPIRE].
D.V. Volkov, Phenomenological Lagrangians, Fiz. Elem. Chast. Atom. Yadra 4 (1973) 3.
T. Hayata, Y. Hidaka, T. Noumi and M. Hongo, Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method, Phys. Rev. D 92 (2015) 065008 [arXiv:1503.04535] [INSPIRE].
M. Hongo, Path-integral formula for local thermal equilibrium, Annals Phys. 383 (2017) 1 [arXiv:1611.07074] [INSPIRE].
M. Hongo, Nonrelativistic hydrodynamics from quantum field theory: (I) Normal fluid composed of spinless Schrödinger fields, arXiv:1801.06520 [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].
A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [arXiv:1501.03845] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R.A. Rosen, More on gapped Goldstones at finite density: More gapped Goldstones, JHEP 11 (2013) 055 [arXiv:1306.1240] [INSPIRE].
A. Nicolis, R. Penco and R.A. Rosen, Relativistic Fluids, Superfluids, Solids and Supersolids from a Coset Construction, Phys. Rev. D 89 (2014) 045002 [arXiv:1307.0517] [INSPIRE].
A. Nicolis, Low-energy effective field theory for finite-temperature relativistic superfluids, arXiv:1108.2513 [INSPIRE].
R.A. Guyer and J.A. Krumhansl, Phenomenological Lagrangians, Phys. Rev. 148 (1966) 778.
S. Huberman, R.A. Duncan, K. Chen, B. Song, V. Chiloyan, Z Ding, A.A. Maznev, G Chen and K.A. Nelson, Observation of second sound in graphite at temperatures above 100 K, Science 364 (2019) 375.
J. Armas and A. Jain, Hydrodynamics for charge density waves and their holographic duals, Phys. Rev. D 101 (2020) 121901 [arXiv:2001.07357] [INSPIRE].
J. Armas and A. Jain, Viscoelastic hydrodynamics and holography, JHEP 01 (2020) 126 [arXiv:1908.01175] [INSPIRE].
V.I. Ogievetsky, Nonlinear realizations of internal and space-time symmetries, in 10th winter school of theoretical physics in Karpacz, Poland. (1974).
E. Ivanov and V. Ogievetsky, The Inverse Higgs Phenomenon in Nonlinear Realizations, Teor. Mat. Fiz. 25 (1975) 1050.
I. Low and A.V. Manohar, Spontaneously broken space-time symmetries and Goldstone’s theorem, Phys. Rev. Lett. 88 (2002) 101602 [hep-th/0110285] [INSPIRE].
S. Endlich, A. Nicolis and R. Penco, Ultraviolet completion without symmetry restoration, Phys. Rev. D 89 (2014) 065006 [arXiv:1311.6491] [INSPIRE].
Steven Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Cambridge University Press, U.K. (1996) DOI.
L.V. Delacrétaz, S. Endlich, A. Monin, R. Penco and F. Riva, (Re-)Inventing the Relativistic Wheel: Gravity, Cosets and Spinning Objects, JHEP 11 (2014) 008 [arXiv:1405.7384] [INSPIRE].
A. Kamenev, Field Theory of Non-Equilibrium Systems, Cambridge University Press, Cambridge, U.K. (2011) DOI.
M. Greiter, F. Wilczek and E. Witten, Hydrodynamic Relations in Superconductivity, Mod. Phys. Lett. B 3 (1989) 903 [INSPIRE].
D.T. Son, Low-energy quantum effective action for relativistic superfluids, hep-ph/0204199 [INSPIRE].
P.C. Martin, O. Parodi and P.S. Pershan, Unified Hydrodynamic Theory for Crystals, Liquid Crystals and Normal Fluids, Phys. Rev. A 2401, (1972) 6.
R. Holyst, A. Poniewierski, On the elastic free energy for smectic-A liquid crystals, J. Phys. II France 3 (1993) 177.
L.P. Pitaevskiῐ, Second Sound in Solids, Sov. Phys. Usp. 342, (1968) 3.
K.B. Efetov, Mean-field thermodynamic quantum time-space crystal: spontaneous breaking of time-translation symmetry in a macroscopic fermion system, Phys. Rev. B 100 (2019) 245128 [arXiv:1905.04128] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2008.11725
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Landry, M.J. Non-equilibrium effective field theory and second sound. J. High Energ. Phys. 2021, 213 (2021). https://doi.org/10.1007/JHEP04(2021)213
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)213
Keywords
- Effective Field Theories
- Quantum Dissipative Systems
- Thermal Field Theory