Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1310.2247 · Journal of High Energy Physics

Superfluid Kubo formulas from partition function

Shira Chapman, Carlos Hoyos, Yaron Oz

Published Apr 1, 2014• 8 citations
arXivHTMLPDF

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.

DOI
10.1007/jhep04(2014)186

Related papers

Kubo formulae for first-order spin hydrodynamics

Jin Chun Hu

We derive Kubo formulae for first-order spin hydrodynamics based on nonequilibrium statistical operators method. In first-order spin hydrodynamics, there are two new transport coefficients besides the ordinary ones appearing in first-order viscous hydrodynamics. They emerge due to the incorporation of the spin degree of freedom into fluids and the spin-orbital coupling. Zubarev's nonequilibrium statistical operator method can be well applied to investigate these quantum effects in fluids. The Kubo formulae, based on the method of nonequilibrium statistical operators, are related to equilibrium (imaginary-time) infrared Green's functions, and all the transport coefficients can be determined when the microscopic theory is specified.

arXiv:2101.08440•Physical review. D/Physical review. D.•Jun 21, 2021•34 citations

Kubo Formulas for Second-Order Hydrodynamic Coefficients

Guy D. Moore, Kiyoumars A. Sohrabi

At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity $\ensuremath{\eta}$ and on five additional ``second-order'' hydrodynamical coefficients ${\ensuremath{\tau}}_{\ensuremath{\Pi}}$, $\ensuremath{\kappa}$, ${\ensuremath{\lambda}}_{1}$, ${\ensuremath{\lambda}}_{2}$, and ${\ensuremath{\lambda}}_{3}$. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient ${\ensuremath{\lambda}}_{3}$ can be evaluated directly by Euclidean means and does not in general vanish.

arXiv:1007.5333•Physical Review Letters•Mar 23, 2011•85 citations

Nonequilibrium steady-state Kubo formula: Equality of transport coefficients

Marko Žnidarič

We address the question of whether transport coefficients obtained from a unitary closed system setting, i.e., the standard equilibrium Green-Kubo formula, are the same as the ones obtained from a weakly driven nonequilibrium steady-state calculation. We first derive a nonequilibrium Kubo-like expression for the steady-state diffusion constant expressed as a time integral of either a current or a conserved density nonequilibrium correlation function. This expression has certain advantages over the equilibrium Green-Kubo formula, but it is not clear if it gives the same value of the diffusion constant. We then rigorously show that if the unitary dynamics is diffusive, the nonequilibrium formula indeed gives exactly the same transport coefficient. The form of finite-size correction is also predicted. Theoretical results are verified by an explicit calculation of the diffusion constant in several interacting many-body models.

arXiv:1806.11050•Physical review. B./Physical review. B•Jan 22, 2019•28 citations

Relativistic second-order spin hydrodynamics: A Kubo-type formulation for the quark-gluon plasma

Duan She, Yi-Wei Qiu, Defu Hou

Building upon Zubarev's nonequilibrium statistical operator formalism, we derive a relativistic canonical-like second-order spin hydrodynamics for two power-counting schemes. We obtain comprehensive second-order expressions for dissipative fluxes, including the shear stress tensor, bulk viscous pressure, charge-diffusion currents, rotational stress tensor, boost heat vector, and spin tensor-related dissipative flux. By introducing novel transport coefficients and expressing them in terms of equilibrium correlation functions, we establish new Kubo-type formulas for second-order transport. Our findings have significant implications for understanding the collective spin dynamics of strongly interacting matter and provide a robust theoretical basis for future experimental and theoretical studies.

arXiv:2410.15142•Physical review. D/Physical review. D.•Feb 21, 2025•10 citations

Dipole superfluid hydrodynamics II

Akash Jain, Kristan Jensen, Ruochuan Liu +1 more

We present a dissipative hydrodynamic theory of "s-wave dipole superfluids" that arise in phases of translation-invariant and dipole-symmetric models in which the U(1) symmetry is spontaneously broken. The hydrodynamic description is subtle on account of an analogue of dangerously irrelevant operators, which requires us to formalize an entirely new derivative counting scheme suitable for these fluids. We use our hydrodynamic model to investigate the linearized response of such a fluid, characterized by sound modes $ω\sim \pm k - ik^2$, shear modes $ω\sim-ik^2$, and magnon-like propagating modes $ω\sim \pm k^2 - ik^4$ that are the dipole-invariant version of superfluid "second sound" modes. We find that these fluids can also admit equilibrium states with "dipole superflow" that resemble a polarized medium. Finally, we couple our theory to slowly varying background fields, which allows us to compute response functions of hydrodynamic operators and Kubo formulas for hydrodynamic transport coefficients.

arXiv:2401.16385•Jan 29, 2024•1 citation

Kubo formula for open finite-size systems

Jinshan Wu, Mona Berciu

We derive a Kubo-type formula that describes proper non-equilibrium stationary states for finite-size systems. We first argue that the usual Kubo formula considers only equilibrium states of the perturbed system, which are inappropriate to describe transport properties. Moreover, we show that the standard Kubo formula for the dc conductance is only appropriate in the thermodynamic limit. We demonstrate that taking into consideration explicitly the coupling to the leads/baths solves both problems. This approach results in well-behaved response functions, without the singular contributions from degenerate states encountered when Kubo formulae for infinite-size systems are inappropriately used for finite-size systems. We also derive a second, more efficient formulation which is valid only for a set of special physical quantities, which includes the charge current density operator.

arXiv:1003.1992•Europhysics Letters (EPL)•Nov 1, 2010•10 citations
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.
We derive Kubo formulae for first-order spin hydrodynamics based on nonequilibrium statistical operators method. In first-order spin hydrodynamics, there are two new transport coefficients besides the ordinary ones appearing in first-order viscous hydrodynamics. They emerge due to the incorporation of the spin degree of freedom into fluids and the spin-orbital coupling. Zubarev's nonequilibrium statistical operator method can be well applied to investigate these quantum effects in fluids. The Kubo formulae, based on the method of nonequilibrium statistical operators, are related to equilibrium (imaginary-time) infrared Green's functions, and all the transport coefficients can be determined when the microscopic theory is specified.
At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity $\ensuremath{\eta}$ and on five additional ``second-order'' hydrodynamical coefficients ${\ensuremath{\tau}}_{\ensuremath{\Pi}}$, $\ensuremath{\kappa}$, ${\ensuremath{\lambda}}_{1}$, ${\ensuremath{\lambda}}_{2}$, and ${\ensuremath{\lambda}}_{3}$. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient ${\ensuremath{\lambda}}_{3}$ can be evaluated directly by Euclidean means and does not in general vanish.
We address the question of whether transport coefficients obtained from a unitary closed system setting, i.e., the standard equilibrium Green-Kubo formula, are the same as the ones obtained from a weakly driven nonequilibrium steady-state calculation. We first derive a nonequilibrium Kubo-like expression for the steady-state diffusion constant expressed as a time integral of either a current or a conserved density nonequilibrium correlation function. This expression has certain advantages over the equilibrium Green-Kubo formula, but it is not clear if it gives the same value of the diffusion constant. We then rigorously show that if the unitary dynamics is diffusive, the nonequilibrium formula indeed gives exactly the same transport coefficient. The form of finite-size correction is also predicted. Theoretical results are verified by an explicit calculation of the diffusion constant in several interacting many-body models.
Building upon Zubarev's nonequilibrium statistical operator formalism, we derive a relativistic canonical-like second-order spin hydrodynamics for two power-counting schemes. We obtain comprehensive second-order expressions for dissipative fluxes, including the shear stress tensor, bulk viscous pressure, charge-diffusion currents, rotational stress tensor, boost heat vector, and spin tensor-related dissipative flux. By introducing novel transport coefficients and expressing them in terms of equilibrium correlation functions, we establish new Kubo-type formulas for second-order transport. Our findings have significant implications for understanding the collective spin dynamics of strongly interacting matter and provide a robust theoretical basis for future experimental and theoretical studies.
We present a dissipative hydrodynamic theory of "s-wave dipole superfluids" that arise in phases of translation-invariant and dipole-symmetric models in which the U(1) symmetry is spontaneously broken. The hydrodynamic description is subtle on account of an analogue of dangerously irrelevant operators, which requires us to formalize an entirely new derivative counting scheme suitable for these fluids. We use our hydrodynamic model to investigate the linearized response of such a fluid, characterized by sound modes ω∼±k−ik2ω\sim \pm k - ik^2ω∼±k−ik2, shear modes ω∼−ik2ω\sim-ik^2ω∼−ik2, and magnon-like propagating modes ω∼±k2−ik4ω\sim \pm k^2 - ik^4ω∼±k2−ik4 that are the dipole-invariant version of superfluid "second sound" modes. We find that these fluids can also admit equilibrium states with "dipole superflow" that resemble a polarized medium. Finally, we couple our theory to slowly varying background fields, which allows us to compute response functions of hydrodynamic operators and Kubo formulas for hydrodynamic transport coefficients.
We derive a Kubo-type formula that describes proper non-equilibrium stationary states for finite-size systems. We first argue that the usual Kubo formula considers only equilibrium states of the perturbed system, which are inappropriate to describe transport properties. Moreover, we show that the standard Kubo formula for the dc conductance is only appropriate in the thermodynamic limit. We demonstrate that taking into consideration explicitly the coupling to the leads/baths solves both problems. This approach results in well-behaved response functions, without the singular contributions from degenerate states encountered when Kubo formulae for infinite-size systems are inappropriately used for finite-size systems. We also derive a second, more efficient formulation which is valid only for a set of special physical quantities, which includes the charge current density operator.