Abstract
We give the free energy of equilibrium relativistic matter subject to external gravitational and electromagnetic fields, to one-derivative order in the gradients of the external fields. The free energy allows for a straightforward derivation of bound currents and bound momenta in equilibrium. At leading order, the energy-momentum tensor admits a simple expression in terms of the polarization tensor. Beyond the leading order, electric and magnetic polarization vectors are intrinsically ambiguous. The physical effects of polarization, such as the correlation between the magneto-vortically induced surface charge and the electro-vortically induced surface current, are not ambiguous.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Jeon and U. Heinz, Introduction to hydrodynamics, Int. J. Mod. Phys. E 24 (2015) 1530010 [arXiv:1503.03931] [INSPIRE].
T. Schäfer and D. Teaney, Nearly perfect fluidity: from cold atomic gases to hot quark gluon plasmas, Rept. Prog. Phys. 72 (2009) 126001 [arXiv:0904.3107] [INSPIRE].
M. Rangamani, Gravity and hydrodynamics: lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].
M. Müller, J. Schmalian and L. Fritz, Graphene: a nearly perfect fluid, Phys. Rev. Lett. 103 (2009) 025301.
A. Lucas, R.A. Davison and S. Sachdev, Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals, arXiv:1604.08598 [INSPIRE].
L.D. Landau and E.M. Lifshitz, Statistical physics, Part I, Pergamon Press, Oxford U.K. (1980).
L.S. Brown, Quantum field theory, Cambridge University Press, Cambridge U.K. (1992).
N. Banerjee et al., 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].
K. Jensen, R. Loganayagam and A. Yarom, Anomaly inflow and thermal equilibrium, JHEP 05 (2014) 134 [arXiv:1310.7024] [INSPIRE].
J. Armas, J. Bhattacharya and N. Kundu, Surface transport in plasma-balls, JHEP 06 (2016) 015 [arXiv:1512.08514] [INSPIRE].
X.G. Wen, Theory of the edge states in fractional quantum Hall effects, Int. J. Mod. Phys. B 06 (1992) 1711.
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].
W. Israel, The dynamics of polarization, Gen. Rel. Grav. 9 (1978) 451 [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Parity-violating hydrodynamics in 2 + 1 dimensions, JHEP 05 (2012) 102 [arXiv:1112.4498] [INSPIRE].
S.R. de Groot and L.G. Suttorp, Foundations of electrodynamics, Horth-Holland, Netherlands (1972).
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: 1606.01226
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
Kovtun, P. Thermodynamics of polarized relativistic matter. J. High Energ. Phys. 2016, 28 (2016). https://doi.org/10.1007/JHEP07(2016)028
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2016)028