Effective field theory of dissipative fluids

Crossley, Michael; Glorioso, Paolo; Liu, Hong

doi:10.48550/arxiv.1511.03646

Cited by 49 publications

(215 citation statements)

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“…Haehl, Loganayagam, and Rangamani (HLR) have classified [25] the most general hydrodynamics consistent with the second Law of thermodynamics, building upon earlier results in hydrostatic equilibrium [26,27]. HLR also obtained Schwinger-Keldysh effective actions [28] for hydrodynamics (see also [29]). A subset of allowed transport (what they dub class L, for Lagrangian) admits an ordinary action via a sigma model, where the fundamental fields are maps from a "reference manifold" to the physical spacetime [25].…”

mentioning

confidence: 90%

Chaos in AdS$_2$ holography

Jensen

2016

Preprint

151

269

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confidence: 90%

Chaos in AdS$_2$ holography

Jensen

2016

Preprint

151

269

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“…To address the subjet of study, we use effective field theory methods, which long ago began to be used in the study of turbulence [63][64][65], and continue to be a powerful tool to study random flows [66][67][68][69]. Among all methods, the Effective Action formalism allows to express the different N-point correlation functions of the theory in terms of loop diagrams, which adds a new source of intuition in the intepretation of the correlations.…”

Section: A Scaling Of the Relevant Diagrams 1 Introductionmentioning

confidence: 99%

Nonlinear Fluctuations in Relativistic Causal Fluids

Mirón-Granese,

Kandus,

Calzetta

2020

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In the Second Order Theories (SOT) of real relativistic fluids, the non-ideal properties of the flows are described by a new set of dynamical tensor variables. In this work we explore the non-linear dynamics of those variables in a conformal fluid. Among all possible SOTs, we choose to work with the Divergence Type Theories (DTT) formalism, which ensures that the second law of thermodynamics is fulfilled non-perturbatively. The tensor modes include two divergence-free modes which have no analog in theories based on covariant generalizations of the Navier-Stokes equation, and that are particularly relevant because they couple linearly to a gravitational field. To study the dynamics of this irreducible tensor sector, we observe that in causal theories such as DTTs, thermal fluctuations induce a stochastic stirring force, which excites the tensor modes while preserving energy momentum conservation. From fluctuation-dissipation considerations it follows that the random force is Gaussian with a white spectrum. The irreducible tensor modes in turn excite vector modes, which back-react on the tensor sector, thus producing a consistent non-linear, second order description of the divergence-free tensor dynamics. Using the Martin-Siggia-Rose (MSR) formalism plus the Two-Particle Irreducible Effective Action (2PIEA) formalism, we obtain the equations for the relevant two-point correlation functions of the model: the retarded propagator and the Hadamard function. The overall result of the self-consistent dynamics of the irreducible tensor modes at this order is a depletion of the relaxation time for the hard modes, a fact that suggests that tensor modes could sustain an inverse cascade of entropy.

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“…This quantum hydrodynamic theory can be considered as a generalization of the conventional hydrodynamics without doing a derivative expansion 4 , and is non-local. Its action, which also incorporates dissipative effects, can be written using the techniques developed in [32,33]. The explicit form of the action S EFT [σ] is not important for our discussion below (we refer interested readers to [21] for details) except that the Lagrangian depends on σ only through derivatives and the equilibrium solution is given by…”

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On systems of maximal quantum chaos

Blake

Liu

2021

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A remarkable feature of chaos in many-body quantum systems is the existence of a bound on the quantum Lyapunov exponent. An important question is to understand what is special about maximally chaotic systems which saturate this bound. Here we provide further evidence for the 'hydrodynamic' origin of chaos in such systems, and discuss hallmarks of maximally chaotic systems. We first provide evidence that a hydrodynamic effective field theory of chaos we previously proposed should be understood as a theory of maximally chaotic systems. We then emphasize and make explicit a signature of maximal chaos which was only implicit in prior literature, namely the suppression of exponential growth in commutator squares of generic few-body operators. We provide a general argument for this suppression within our chaos effective field theory, and illustrate it using SYK models and holographic systems. We speculate that this suppression indicates that the nature of operator scrambling in maximally chaotic systems is fundamentally different to scrambling in non-maximally chaotic systems. We also discuss a simplest scenario for the existence of a maximally chaotic regime at sufficiently large distances even for non-maximally chaotic systems.

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Effective field theory of dissipative fluids

Cited by 49 publications

References 2 publications

Chaos in AdS$_2$ holography

Chaos in AdS$_2$ holography

Nonlinear Fluctuations in Relativistic Causal Fluids

On systems of maximal quantum chaos

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