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:1311.3333

Quantum ideal hydrodynamics on the lattice

Tommy Burch, Giorgio Torrieri

Published Nov 13, 2013• 0 citations
arXivHTMLPDF

Abstract

After discussing the problem of defining the hydrodynamic limit from microscopic scales, we give an introduction to ideal hydrodynamics in the Lagrange picture, and show that it can be viewed as a field theory, which can be quantized using the usual Feynman sum-over-paths prescription. We then argue that this picture can be connected to the usually neglected thermal microscopic scale in the hydrodynamic expansion. After showing that this expansion is generally non-perturbative, we show how the lattice can be used to understand the impact quantum and thermal fluctuations can have on the fluid behavior.

DOI
10.48550/arxiv.1311.3333

Related papers

Hydrodynamics and thermalization

Esteban Calzetta, B. L. Hu

Since the systems described by quantum fields are by definition extended, it is natural to think that in some limit they may reasonably well be approximated as fluids. This means that the state of the system is parameterized by a few locally well-defined fields such as temperature or energy density, obeying a set of hyperbolic equations of motion. A concrete example is the extensive use of fluid models to describe high-energy collisions [BelLan56, CarDuo73, CoFrSc74, Bjo83, CarZac83]. Our earlier derivation of quantum kinetic theory suggests a way to put this insight on a formal basis. Within its range of validity, the Boltzmann equation will drive the one-particle distribution function towards local thermal equilibrium. On scales much larger than the local thermalization scale, we expect to see hydrodynamical behavior [BeCoPa02]. This is, after all, the usual way of deriving hydrodynamics from kinetic theory [Hua87]. Beware, notwithstanding, that even at the level of classical kinetic theory there are still open questions regarding the cross-over from the kinetic to the hydro regime [KarGor02, KarGor03]. If we understand hydrodynamics as stated in the first paragraph of this chapter, then a system defined in terms of a quantum field may not have a hydrodynamic limit. This has been shown in [Elz02] for the case of a free Fermi field.

Cambridge University Press eBooks•Jul 24, 2008•0 citations

Quantum vorticity: A not so effective field theory

Gabriel Cuomo, Fanny Eustachon, Eren Firat +2 more

We provide a comprehensive picture for the formulation of the perfect fluid in the modern effective field theory formalism at both the classical and quantum level. Due to the necessity of decomposing the hydrodynamical variables (\rho, p, u^\mu) ( ρ , p , u μ ) into other internal degrees of freedom, the procedure is inherently not unique. We discuss and compare the different inequivalent formulations. These theories possess a peculiarity: the presence of an infinite dimensional symmetry implying a vanishing dispersion relation \omega = 0 ω = 0 for the transverse modes. This sets the stage for UV-IR mixing in the quantum theory, which we study in the different formulations focussing on the incompressible limit. We observe that the dispersion relation gets modified by quantum effects to become \omega \propto k^2 ω ∝ k 2 , where the fundamental excitations can be viewed as vortex-anti-vortex pairs. The spectrum exhibits infinitely many types of degenerate quanta. The unusual sensitivity to UV quantum fluctuations renders the implementation of the defining infinite symmetry somewhat subtle. However we present a lattice regularization that preserves a deformed version of such symmetry.

arXiv:2412.10344•SciPost Physics•Jan 21, 2026•3 citations

All-order fluctuating hydrodynamics of the SYK lattice

Marta Bucca, Akash Jain, Márk Mezei +1 more

The SYK model has played an important role in recent developments in many-body quantum chaos. We study a spatially local generalisation of it: the SYK lattice. Starting from the nonlinear action of pseudo-Goldstone bosons that dominate its dynamics at low temperatures, in the long wavelength limit we reorganise this action as the effective field theory for fluctuating hydrodynamics, thereby showing how the hydrodynamic degrees of freedom embed into the microscopic description of the model. We compute the hydrodynamic effective action to high orders in the derivative expansion and determine all the corresponding transport coefficients. Hence this work derives hydrodynamics from the microscopic description of a strongly coupled quantum many-body system.

arXiv:2604.18675•Apr 20, 2026•0 citations

Application of the theory of C*-algebras to the emergence of hydrodynamics in quantum many-body systems

Dimitrios Ampelogiannis

This Ph.D. thesis reports on progress in rigorously establishing hydrodynamic principles from the microscopic Hamiltonian dynamics of quantum many-body systems in a general, non-model-specific manner. Using the C*-algebra framework of statistical mechanics, we treat systems directly in the thermodynamic limit, primarily focusing on quantum lattice models where tools such as Lieb-Robinson bounds yield rigorous statements. We thus provide a proof-of-principle that large-scale behaviours can indeed be seen as emerging from microscopic dynamics, with mathematical proof. We first report on ergodicity results in short-range models with exponentially decaying or finite-range interactions. We show that time-averaged observables converge to their ensemble averages and decorrelate from all other observables almost everywhere within the light-cone defined by Lieb-Robinson bounds. This relaxation property indicates the loss of information at large scales, from which we prove a Boltzmann-Gibbs principle: at the Euler scaling limit of large time and distance, observables project onto hydrodynamic modes (extensive conserved quantities), within correlation functions. These results hold independently of microscopic details, capturing the physical idea that such details are lost at large space-time scales. Regarding finer scales of hydrodynamics, we discuss rigorous lower bounds on the strength of diffusion. We establish a general result on the clustering of n-th order connected correlations within C* dynamical systems. These results are applied to obtain a strictly positive lower bound on the diffusion constant of chaotic open quantum spin chains with nearest-neighbor interactions. This thesis underlines the universality of hydrodynamic principles, provides a framework for establishing them rigorously, and sets the stage for future progress toward the goal of proving the hydrodynamic equations.

arXiv:2601.08601•Jan 13, 2026•0 citations

A quantum theory for non-viscous fluids in the Lagrange variables

S. F. B. Tyabji

1. Introduction. A number of authors (2,3,7) have recently quantized the motion of an inviscid fluid. The starting point has been the variational principle of Bateman which uses the Clebsch variables. The density turns out to be the canonical conjugate to the velocity potential, and the transition to the quantum theory is then made in the usual way. If the fluid is making small vibrations, ‘phonons’, which are scalar, appear as a result of the quantization.

Mathematical Proceedings of the Cambridge Philosophical Society•Jul 1, 1954•4 citations

Boulder Lectures on Thermal Dynamics and Hydrodynamic EFTs

Luca V. Delacrétaz

Fluctuating hydrodynamics emerges in essentially any local many-body system at nonzero temperature. Effective field theory (EFT) approaches enable the quantitative study of this emergence, providing a controlled framework to capture late-time observables. These lectures introduce the organizing principles behind equilibrium and out-of-equilibrium dynamics in these thermalizing systems. A central focus is the modern construction of these EFTs, which frames fluctuating hydrodynamics through the lens of "strong-to-weak" spontaneous symmetry breaking. Drawing examples from both high-energy and condensed matter physics, we show how this paradigm adapts to systems ranging from spin chains to relativistic quantum field theories, including models with generalized symmetries or symmetries with 't Hooft anomalies. Finally, we discuss UV/IR constraints on transport parameters -- viewed as the Wilson coefficients of hydrodynamic EFTs -- both in continuum and on the lattice.

arXiv:2606.02391•Jun 1, 2026•0 citations
After discussing the problem of defining the hydrodynamic limit from microscopic scales, we give an introduction to ideal hydrodynamics in the Lagrange picture, and show that it can be viewed as a field theory, which can be quantized using the usual Feynman sum-over-paths prescription. We then argue that this picture can be connected to the usually neglected thermal microscopic scale in the hydrodynamic expansion. After showing that this expansion is generally non-perturbative, we show how the lattice can be used to understand the impact quantum and thermal fluctuations can have on the fluid behavior.
Since the systems described by quantum fields are by definition extended, it is natural to think that in some limit they may reasonably well be approximated as fluids. This means that the state of the system is parameterized by a few locally well-defined fields such as temperature or energy density, obeying a set of hyperbolic equations of motion. A concrete example is the extensive use of fluid models to describe high-energy collisions [BelLan56, CarDuo73, CoFrSc74, Bjo83, CarZac83]. Our earlier derivation of quantum kinetic theory suggests a way to put this insight on a formal basis. Within its range of validity, the Boltzmann equation will drive the one-particle distribution function towards local thermal equilibrium. On scales much larger than the local thermalization scale, we expect to see hydrodynamical behavior [BeCoPa02]. This is, after all, the usual way of deriving hydrodynamics from kinetic theory [Hua87]. Beware, notwithstanding, that even at the level of classical kinetic theory there are still open questions regarding the cross-over from the kinetic to the hydro regime [KarGor02, KarGor03]. If we understand hydrodynamics as stated in the first paragraph of this chapter, then a system defined in terms of a quantum field may not have a hydrodynamic limit. This has been shown in [Elz02] for the case of a free Fermi field.
We provide a comprehensive picture for the formulation of the perfect fluid in the modern effective field theory formalism at both the classical and quantum level. Due to the necessity of decomposing the hydrodynamical variables (\rho, p, u^\mu) ( ρ , p , u μ ) into other internal degrees of freedom, the procedure is inherently not unique. We discuss and compare the different inequivalent formulations. These theories possess a peculiarity: the presence of an infinite dimensional symmetry implying a vanishing dispersion relation \omega = 0 ω = 0 for the transverse modes. This sets the stage for UV-IR mixing in the quantum theory, which we study in the different formulations focussing on the incompressible limit. We observe that the dispersion relation gets modified by quantum effects to become \omega \propto k^2 ω ∝ k 2 , where the fundamental excitations can be viewed as vortex-anti-vortex pairs. The spectrum exhibits infinitely many types of degenerate quanta. The unusual sensitivity to UV quantum fluctuations renders the implementation of the defining infinite symmetry somewhat subtle. However we present a lattice regularization that preserves a deformed version of such symmetry.
The SYK model has played an important role in recent developments in many-body quantum chaos. We study a spatially local generalisation of it: the SYK lattice. Starting from the nonlinear action of pseudo-Goldstone bosons that dominate its dynamics at low temperatures, in the long wavelength limit we reorganise this action as the effective field theory for fluctuating hydrodynamics, thereby showing how the hydrodynamic degrees of freedom embed into the microscopic description of the model. We compute the hydrodynamic effective action to high orders in the derivative expansion and determine all the corresponding transport coefficients. Hence this work derives hydrodynamics from the microscopic description of a strongly coupled quantum many-body system.
This Ph.D. thesis reports on progress in rigorously establishing hydrodynamic principles from the microscopic Hamiltonian dynamics of quantum many-body systems in a general, non-model-specific manner. Using the C*-algebra framework of statistical mechanics, we treat systems directly in the thermodynamic limit, primarily focusing on quantum lattice models where tools such as Lieb-Robinson bounds yield rigorous statements. We thus provide a proof-of-principle that large-scale behaviours can indeed be seen as emerging from microscopic dynamics, with mathematical proof. We first report on ergodicity results in short-range models with exponentially decaying or finite-range interactions. We show that time-averaged observables converge to their ensemble averages and decorrelate from all other observables almost everywhere within the light-cone defined by Lieb-Robinson bounds. This relaxation property indicates the loss of information at large scales, from which we prove a Boltzmann-Gibbs principle: at the Euler scaling limit of large time and distance, observables project onto hydrodynamic modes (extensive conserved quantities), within correlation functions. These results hold independently of microscopic details, capturing the physical idea that such details are lost at large space-time scales. Regarding finer scales of hydrodynamics, we discuss rigorous lower bounds on the strength of diffusion. We establish a general result on the clustering of n-th order connected correlations within C* dynamical systems. These results are applied to obtain a strictly positive lower bound on the diffusion constant of chaotic open quantum spin chains with nearest-neighbor interactions. This thesis underlines the universality of hydrodynamic principles, provides a framework for establishing them rigorously, and sets the stage for future progress toward the goal of proving the hydrodynamic equations.
Fluctuating hydrodynamics emerges in essentially any local many-body system at nonzero temperature. Effective field theory (EFT) approaches enable the quantitative study of this emergence, providing a controlled framework to capture late-time observables. These lectures introduce the organizing principles behind equilibrium and out-of-equilibrium dynamics in these thermalizing systems. A central focus is the modern construction of these EFTs, which frames fluctuating hydrodynamics through the lens of "strong-to-weak" spontaneous symmetry breaking. Drawing examples from both high-energy and condensed matter physics, we show how this paradigm adapts to systems ranging from spin chains to relativistic quantum field theories, including models with generalized symmetries or symmetries with 't Hooft anomalies. Finally, we discuss UV/IR constraints on transport parameters -- viewed as the Wilson coefficients of hydrodynamic EFTs -- both in continuum and on the lattice.