Lecture notes on Generalised Hydrodynamics

Doyon, Benjamin

doi:10.21468/scipostphyslectnotes.18

Cited by 192 publications

(247 citation statements)

References 153 publications

(387 reference statements)

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“…Given the initial state defined by (19) with smooth profiles β(⋅), we consider the Euler-scale hydrodynamic approximation [3,35] ⟨O Tr e −G β(x,t) (22) for O = O(0, 0) with…”

Section: Euler-scale Ghdmentioning

confidence: 99%

“…Given our generalized Gibbs ensemble Q, following [3], the associated Euler-scale hydrodynamic equations are 8 We note that, for (r ′ , p ′ ), (r ′′ , p ′′ ) ∈ I and t) and A r ′′ r ′ (x, t) are referred to as flux Jacobians. To solve these equations, we note that (15) implies…”

Section: Hydrodynamic Equationsmentioning

confidence: 99%

“…r ′ ,p ′ and A r ′′ r ′ (x, t) = A r ′′ r ′ are diagonal 9 and independent of (x, t), and thus obviously independent of ⟨q r ′ ,p ′ ⟩ β(x,t) and ⟨q J r ′ ⟩ β(x,t) , respectively. This simplifies the treatment considerably compared to the general situation, see, e.g., [3].…”

Section: Hydrodynamic Equationsmentioning

confidence: 99%

“…Recent years have witnessed new advances in the application of hydrodynamics to study 1+1dimensional quantum (and classical) many-body systems out of equilibrium. One such development is generalized hydrodynamics (GHD) [1,2], which extends conventional hydrodynamics by taking into account the macroscopically large number of conserved charges characteristic of integrable systems, see [3] for a pedagogical overview. Since proposed, GHD has attracted considerable interest, see, e.g., [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], and its predictions were recently verified experimentally [21].…”

Section: Introductionmentioning

confidence: 99%

“…In Sec. 3, following [3], the associated hydrodynamic equations are derived and solved exactly. In Sec.…”

Section: Introductionmentioning

confidence: 99%

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Emergence of generalized hydrodynamics in the non-local Luttinger model

Moosavi

2020

SciPost Phys.

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We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.

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“…Given the initial state defined by (19) with smooth profiles β(⋅), we consider the Euler-scale hydrodynamic approximation [3,35] ⟨O Tr e −G β(x,t) (22) for O = O(0, 0) with…”

Section: Euler-scale Ghdmentioning

confidence: 99%

Section: Hydrodynamic Equationsmentioning

confidence: 99%

Section: Hydrodynamic Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In Sec. 3, following [3], the associated hydrodynamic equations are derived and solved exactly. In Sec.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Emergence of generalized hydrodynamics in the non-local Luttinger model

Moosavi

2020

SciPost Phys.

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Mesoscale Mode Coupling Theory for the Weakly Asymmetric Simple Exclusion Process

Schütz

2024

Springer Proceedings in Mathematics &Amp; Statistics

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Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

Ubaldo

Policastro

2023

J. High Energ. Phys.

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We consider the generalization of a matrix integral with arbitrary spectral curve ρ0(E) to a 0+1D theory of matrix quantum mechanics (MQM). Using recent techniques for 1D quantum systems at large-N, we formulate a hydrodynamical effective theory for the eigenvalues. The result is a simple 2D free boson BCFT on a curved background, describing the quantum fluctuations of the eigenvalues around ρ0(E), which is now the large-N limit of the quantum expectation value of the eigenvalue density operator $$ \hat{\rho}(E) $$ ρ ̂ E .The average over the ensemble of random matrices becomes a quantum expectation value. Equal-time density correlations reproduce the results (including non-perturbative corrections) of random matrix theory. This suggests an interpretation of JT gravity as dual to a one-time-point reduction of MQM.As an application, we compute the Rényi entropy associated to a bipartition of the eigenvalues. We match a previous result by Hartnoll and Mazenc for the c = 1 matrix model dual to two-dimensional string theory and extend it to arbitrary ρ0(E). The hydrodynamical theory provides a clear picture of the emergence of spacetime in two dimensional string theory. The entropy is naturally finite and displays a large amount of short range entanglement, proportional to the microcanonical entropy. We also compute the reduced density matrix for a subset of n < N eigenvalues.

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Lecture notes on Generalised Hydrodynamics

Cited by 192 publications

References 153 publications

Emergence of generalized hydrodynamics in the non-local Luttinger model

Emergence of generalized hydrodynamics in the non-local Luttinger model

Mesoscale Mode Coupling Theory for the Weakly Asymmetric Simple Exclusion Process

Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

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