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We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems.
Theory of thermal transport coefficients
J. Luttinger · 1964
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Gravitation and Cosmology
S. Weinberg · 1972
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Theory of quantised Hall conductivity in two dimensions
P. Streda · 1982
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Thermodynamic derivation of the Hall current and the thermopower in quantising
P. Streda and L. Smrcka · 1983
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Quantized Hall effect and edge currents
A. H. MacDonald and P. Středa · 1984
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Fluid mechanics
L. Landau and E. Lifshitz · 1987
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Thermoelectric response of an interacting two-dimensional electron gas in a quantizing magnetic field
N. R. Cooper, B. I. Halperin, and I. M. Ruzin · 1997
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Energy Magnetization and the Thermal Hall Effect
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Towards hydrodynamics without an entropy current
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Constraints on fluid dynamics from equilibrium partition functions
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Cross-Correlated Responses of Topological Superconductors and Superfluids
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Newton-Cartan Geometry and the Quantum Hall Effect
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On Nonrelativistic Diffeomorphism Invariance
O. Andreev, M. Haack, and S. Hofmann · 2013
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Torsional Newton-Cartan geometry and Lifshitz holography
M. H. Christensen, J. Hartong, N. A. Obers, and B. Rollier · 2014
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A. G. Abanov and A. Gromov · 2014
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Parity-violating hydrodynamics in 2 + 1 dimensions
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Cited in the paper.
It is often convenient to define the “inverse metric” h μ ν = e μ A e ν A h_{\mu\nu}=e^{A}_{\mu}e^{A}_{\nu} . It satisfies h μ ν h ν ρ = δ ρ μ − v μ n ρ h^{\mu\nu}h_{\nu\rho}=\delta^{\mu}_{\rho}-v^{\mu}n_{\rho} and h μ ν v μ = 0 h_{\mu\nu}v^{\mu}=0 and is fully determined by v μ , n ν v^{\mu},n_{\nu} and h i j h^{ij}
Cited in the paper.
As d 𝒫 = − s d T − n d μ − M d ℬ − M E d Ω d\mathcal{P}=-sdT-nd\mu-Md\mathcal{B}-M_{E}d\Omega we have ∂ M / ∂ μ = ∂ n / ∂ B \partial M/\partial\mu=\partial n/\partial B etc
Cited in the paper.
In preparation
B. Bradlyn and N. Read
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Density-curvature response and gravitational anomaly
A. Gromov and A. G. Abanov · 2014
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Spacetime Symmetries of the Quantum Hall Effect
M. Geracie, D. Son, C. Wu, and S.-F. Wu · 2014
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