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

Particles

Reworking Zubarev’s Approach to Nonequilibrium Quantum Statistical Mechanics

F. Becattini, Matteo Buzzegoli, Eduardo Grossi

Published Apr 8, 2019• 73 citations
Publisher

Abstract

In this work, the nonequilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at a local thermodynamic equilibrium is revisited. This method, which was used to obtain the first “Kubo” formula of shear viscosity, is especially suitable to describe quantum effects in fluids. This feature makes it a viable tool to describe the physics of Quark–Gluon Plasma in relativistic nuclear collisions.

DOI
10.3390/particles2020014

Related papers

Reworking the Zubarev's approach to non-equilibrium quantum statistical mechanics

F. Becattini, Matteo Buzzegoli, Eduardo Grossi

In this work the non-equilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at local thermodynamic equilibrium is revisited. This method - which was used to obtain the first ''Kubo" formula of shear viscosity, is especially suitable to describe quantum effects in fluids. This feature makes it a viable tool to describe the physics of the Quark Gluon Plasma in relativistic nuclear collisions.

arXiv:1902.01089•Feb 4, 2019•5 citations

Nonequilibrium Phenomena in Strongly Correlated Systems

David Bernhard Blaschke, Alexandra V. Friesen, V. G. Morozov +2 more

The book is devoted to the fundamental aspects of the non-equilibrium statistical mechanics of many-particle systems. The concept of Zubarev's approach, which generalizes the notion of Gibbs' ensembles, and introduces a nonequilibrium statistical operator, providing an adequate basis for dealing with strongly correlated systems that are governed by nonperturbative phenomena, such as the formation of bound states, quantum condensates and the instability of the vacuum. Besides a general introduction to the formalism, this book contains contributions devoted to the applications of Zubarev's method to the solution of modern problems in different fields of physics: transport theory, hydrodynamics, high-energy physics, quark-gluon plasma and hadron production in heavy-ion collisions. The book provides valuable information for researchers and students in these fields, requiring powerful concepts to solve fundamental problems of non-equilibrium phenomena in strongly

MDPI eBooks•Sep 28, 2020•1 citation

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

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

Shear Viscosity of Nonequilibrium Scalar Field Theory

A. A. Radovskaya, Andrew G. Semenov

Abstract Shear viscosity of a nonequilibrium quantum field φ4 is considered in the framework of the Classical statistical approximation. The dependence on the initial energy distribution is investigated. The generalisation of the Green–Kubo relation to the case of the stationary nonequilibrium field is obtained.

Physics of Particles and Nuclei•Jul 1, 2021•3 citations

Viscosity of strongly interacting quantum fluids: Spectral functions and sum rules

Edward Taylor, Mohit Randeria

The viscosity of strongly interacting systems is a topic of great interest in diverse fields. We focus here on the bulk and shear viscosities of nonrelativistic quantum fluids, with particular emphasis on strongly interacting ultracold Fermi gases. We use Kubo formulas for the bulk and shear viscosity spectral functions, $\ensuremath{\zeta}(\ensuremath{\omega})$ and $\ensuremath{\eta}(\ensuremath{\omega})$, respectively, to derive exact, nonperturbative results. Our results include a microscopic connection between the shear viscosity $\ensuremath{\eta}$ and the normal-fluid density ${\ensuremath{\rho}}_{n}$; sum rules for $\ensuremath{\zeta}(\ensuremath{\omega})$ and $\ensuremath{\eta}(\ensuremath{\omega})$ and their evolution through the BCS-BEC crossover (where BEC denotes Bose-Einstein condensate); and universal high-frequency tails for $\ensuremath{\eta}(\ensuremath{\omega})$ and the dynamic structure factor $S(\mathbf{q},\ensuremath{\omega})$. We use our sum rules to show that, at unitarity, $\ensuremath{\zeta}(\ensuremath{\omega})$ is identically zero and thus relate $\ensuremath{\eta}(\ensuremath{\omega})$ to density-density correlations. We predict that frequency-dependent shear viscosity $\ensuremath{\eta}(\ensuremath{\omega})$ of the unitary Fermi gas can be experimentally measured using Bragg spectroscopy.

arXiv:1002.0869•Physical Review A•May 11, 2010•114 citations
In this work, the nonequilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at a local thermodynamic equilibrium is revisited. This method, which was used to obtain the first “Kubo” formula of shear viscosity, is especially suitable to describe quantum effects in fluids. This feature makes it a viable tool to describe the physics of Quark–Gluon Plasma in relativistic nuclear collisions.
The book is devoted to the fundamental aspects of the non-equilibrium statistical mechanics of many-particle systems. The concept of Zubarev's approach, which generalizes the notion of Gibbs' ensembles, and introduces a nonequilibrium statistical operator, providing an adequate basis for dealing with strongly correlated systems that are governed by nonperturbative phenomena, such as the formation of bound states, quantum condensates and the instability of the vacuum. Besides a general introduction to the formalism, this book contains contributions devoted to the applications of Zubarev's method to the solution of modern problems in different fields of physics: transport theory, hydrodynamics, high-energy physics, quark-gluon plasma and hadron production in heavy-ion collisions. The book provides valuable information for researchers and students in these fields, requiring powerful concepts to solve fundamental problems of non-equilibrium phenomena in strongly
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.
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.
The viscosity of strongly interacting systems is a topic of great interest in diverse fields. We focus here on the bulk and shear viscosities of nonrelativistic quantum fluids, with particular emphasis on strongly interacting ultracold Fermi gases. We use Kubo formulas for the bulk and shear viscosity spectral functions, $\ensuremath{\zeta}(\ensuremath{\omega})$ and $\ensuremath{\eta}(\ensuremath{\omega})$, respectively, to derive exact, nonperturbative results. Our results include a microscopic connection between the shear viscosity $\ensuremath{\eta}$ and the normal-fluid density ${\ensuremath{\rho}}_{n}$; sum rules for $\ensuremath{\zeta}(\ensuremath{\omega})$ and $\ensuremath{\eta}(\ensuremath{\omega})$ and their evolution through the BCS-BEC crossover (where BEC denotes Bose-Einstein condensate); and universal high-frequency tails for $\ensuremath{\eta}(\ensuremath{\omega})$ and the dynamic structure factor $S(\mathbf{q},\ensuremath{\omega})$. We use our sum rules to show that, at unitarity, $\ensuremath{\zeta}(\ensuremath{\omega})$ is identically zero and thus relate $\ensuremath{\eta}(\ensuremath{\omega})$ to density-density correlations. We predict that frequency-dependent shear viscosity $\ensuremath{\eta}(\ensuremath{\omega})$ of the unitary Fermi gas can be experimentally measured using Bragg spectroscopy.