Abstract
Linear response theory relates hydrodynamic transport coefficients to equilibrium retarded correlation functions of the stress-energy tensor and global symmetry currents in terms of Kubo formulas. Some of these transport coefficients are non-dissipative and affect the fluid dynamics at equilibrium. We present an algebraic framework for deriving Kubo formulas for such thermal transport coefficients by using the equilibrium partition function. We use the framework to derive Kubo formulas for all such transport coefficients of superfluids, as well as to rederive Kubo formulas for various normal fluid systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Banerjee et al., Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
K. Jensen et al., Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
G.D. Moore and K.A. Sohrabi, Kubo Formulae for Second-Order Hydrodynamic Coefficients, Phys. Rev. Lett. 106 (2011) 122302 [arXiv:1007.5333] [INSPIRE].
G.D. Moore and K.A. Sohrabi, Thermodynamical second-order hydrodynamic coefficients, JHEP 11 (2012) 148 [arXiv:1210.3340] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A Theory of first order dissipative superfluid dynamics, arXiv:1105.3733 [INSPIRE].
Y. Neiman and Y. Oz, Anomalies in Superfluids and a Chiral Electric Effect, JHEP 09 (2011) 011 [arXiv:1106.3576] [INSPIRE].
S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions, JHEP 01 (2013) 040 [arXiv:1206.6106] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational Anomaly and Transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
I. Amado, K. Landsteiner and F. Pena-Benitez, Anomalous transport coefficients from Kubo formulas in Holography, JHEP 05 (2011) 081 [arXiv:1102.4577] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalous Transport from Kubo Formulae, Lect. Notes Phys. 871 (2013) 433 [arXiv:1207.5808] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya and S. Minwalla, Dissipative Superfluid dynamics from gravity, JHEP 04 (2011) 125 [arXiv:1101.3332] [INSPIRE].
H. Guo, Ch.-Ch. Chien and Y. He, Gauge-invariant linear response theory of relativistic Bardeen-Cooper-Schrieffer superfluids, Phys. Rev. D 85 (2012) 074025 [arXiv:1202.5234].
M. Luzum and P. Romatschke, Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at \( \sqrt{{{s_{{N\,N}}}}} \) = 200-GeV, Phys. Rev. C 78 (2008) 034915 [Erratum ibid. C 79 (2009)039903] [arXiv:0804.4015] [INSPIRE].
N. Banerjee, S. Dutta, S. Jain, R. Loganayagam and T. Sharma, Constraints on Anomalous Fluid in Arbitrary Dimensions, JHEP 03 (2013) 048 [arXiv:1206.6499] [INSPIRE].
A. Meyer and Y. Oz, Constraints on Rindler Hydrodynamics, JHEP 07 (2013) 090 [arXiv:1304.6305] [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
Y. Neiman and Y. Oz, Relativistic Hydrodynamics with General Anomalous Charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].
K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Holographic Gravitational Anomaly and Chiral Vortical Effect, JHEP 09 (2011) 121 [arXiv:1107.0368] [INSPIRE].
S. Chapman, Y. Neiman and Y. Oz, Fluid/Gravity Correspondence, Local Wald Entropy Current and Gravitational Anomaly, JHEP 07 (2012) 128 [arXiv:1202.2469] [INSPIRE].
S. Golkar and D.T. Son, Non-Renormalization of the Chiral Vortical Effect Coefficient, arXiv:1207.5806 [INSPIRE].
D.-F. Hou, H. Liu and H.-c. Ren, A Possible Higher Order Correction to the Vortical Conductivity in a Gauge Field Plasma, Phys. Rev. D 86 (2012) 121703 [arXiv:1210.0969] [INSPIRE].
K. Jensen, Triangle Anomalies, Thermodynamics and Hydrodynamics, Phys. Rev. D 85 (2012) 125017 [arXiv:1203.3599] [INSPIRE].
K. Jensen et al., Parity-Violating Hydrodynamics in 2+1 Dimensions, JHEP 05 (2012) 102 [arXiv:1112.4498] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1310.2247
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Chapman, S., Hoyos, C. & Oz, Y. Superfluid Kubo formulas from partition function. J. High Energ. Phys. 2014, 186 (2014). https://doi.org/10.1007/JHEP04(2014)186
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2014)186