Lecture notes on Generalised Hydrodynamics

Abstract

These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo Institute of Technology, October 2019. I overview in a pedagogical fashion the main aspects of the theory of generalised hydrodynamics, a hydrodynamic theory for quantum and classical many-body integrable systems. Only very basic knowledge of hydrodynamics and integrable systems is assumed.

v1: 87 pages, 17 figures. v2: 96 pages, 18 figures, citations added, typos corrected, subsection 1.1 added (4 pages), version as published in SciPost Phys. Lect. Notes

References in corpus (22)

• The large deviation approach to statistical mechanics
• Experimental Observation of a Generalized Gibbs Ensemble
• Hydrodynamics of electrons in graphene
• "Light-cone" dynamics after quantum quenches in spin chains
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Quantum Generalized Hydrodynamics
• Hydrodynamics in graphene: Linear-response transport
• Diffusive hydrodynamics from integrability breaking
• Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Kardar-Parisi-Zhang universality from soft gauge modes
• Current fluctuations for anharmonic chains in thermal equilibrium
• Current operators in integrable spin chains: lessons from long range deformations
• Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents
• Long-Time Asymptotics of the Toda Lattice for Decaying Initial Data Revisited
• The collision rate ansatz for the classical Toda lattice
• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
• Non-Equilibrium Conformal Field Theories with Impurities
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions
• The Whitham Approach to the $c\to 0$ limit of The Lieb-Liniger Model and Generalized Hydrodynamics
• Exact finite volume expectation values of conserved currents

Cited by in corpus (164)

• Random Quantum Circuits
• Finite-temperature transport in one-dimensional quantum lattice models
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Growth of entanglement entropy under local projective measurements
• Superdiffusion in spin chains
• Correlation functions and transport coefficients in generalised hydrodynamics
• Microscopic origin of the quantum Mpemba effect in integrable systems
• Superuniversality of superdiffusion
• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Hydrodynamics of weak integrability breaking
• Soliton gas in integrable dispersive hydrodynamics
• Symmetry restoration and quantum Mpemba effect in symmetric random circuits
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• Stability of superdiffusion in nearly integrable spin chains
• Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems
• Entanglement spreading in non-equilibrium integrable systems
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Ballistic macroscopic fluctuation theory
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
• Inhomogeneous conformal field theory out of equilibrium
• A short introduction to Generalized Hydrodynamics
• Absence of Normal Fluctuations in an Integrable Magnet
• Generalized hydrodynamics of the KdV soliton gas
• Hydrodynamic projections and the emergence of linearised Euler equations in one-dimensional isolated systems
• Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
• Dynamics of charge fluctuations from asymmetric initial states
• Anomalous transport from hot quasiparticles in interacting spin chains
• Form factors and generalized hydrodynamics for integrable systems
• Generalized hydrodynamics: a perspective
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• Direct observation of hydrodynamization and local prethermalization
• Hydrodynamics of nonintegrable systems from a relaxation-time approximation
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
• Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems
• Euler-scale dynamical correlations in integrable systems with fluid motion
• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
• Quantum Mpemba Effects from Symmetry Perspectives
• Thermalization of interacting quasi-one-dimensional systems
• $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
• Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation
• Can the Macroscopic Fluctuation Theory be Quantized?
• Real-Time Evolution in the Hubbard Model with Infinite Repulsion
• Solution of the BEC to BCS Quench in One Dimension
• Operator front broadening in chaotic and integrable quantum chains
• Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation
• Hydrodynamics in long-range interacting systems with center-of-mass conservation
• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
• Hydrodynamics and the eigenstate thermalization hypothesis
• Interface dynamics in the two-dimensional quantum Ising model
• Finite temperature dynamics in gapped 1D models in the sine-Gordon family
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• Probing the local rapidity distribution of a 1D Bose gas
• The hydrodynamic theory of dynamical correlation functions in the XX chain
• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• Tuning the Quantum Mpemba Effect in Isolated System by Initial State Engineering
• Full Counting Statistics of Charge in Quenched Quantum Gases
• Space-time observation of the dynamics of soliton collisions in a recirculating optical fiber loop
• Scaling of fronts and entanglement spreading during a domain wall melting
• Exact large-scale fluctuations of the phase field in the sine-Gordon model
• Comparing numerical methods for hydrodynamics in a one-dimensional lattice spin model
• Thermodynamics and fractal Drude weights in the sine-Gordon model
• Diffusive hydrodynamics from long-range correlations
• Effects of atom losses on a one-dimensional lattice gas of hardcore bosons
• Symmetry Breaking Dynamics in Quantum Many-Body Systems
• Popcorn Drude weights from quantum symmetry
• Slow crossover from superdiffusion to diffusion in isotropic spin chains
• The Whitham approach to Generalized Hydrodynamics
• Long-lived Solitons and Their Signatures in the Classical Heisenberg Chain
• Non-equilibrium steady state formation in 3+1 dimensions
• Anisotropic Landau-Lifshitz Model in Discrete Space-Time
• Integrability breaking in the Rule 54 cellular automaton
• Current correlations, Drude weights and large deviations in a box-ball system
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• New classical integrable systems from generalized $T\bar{T}$-deformations
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Iterative construction of conserved quantities in dissipative nearly integrable systems
• Quench dynamics in lattices above one dimension: the free fermionic case
• Finite temperature equilibrium density profiles of integrable systems in confining potentials
• Benchmarks of Generalized Hydrodynamics for 1D Bose Gases
• Navier-Stokes equations for nearly integrable quantum gases
• Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, Circular $\beta$-ensemble and double confluent Heun equation
• Large Deviations for Ablowitz-Ladik lattice, and the Schur flow
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Slow thermalization and subdiffusion in $U(1)$ conserving Floquet random circuits
• Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model
• Translation symmetry restoration in integrable systems: the noninteracting case
• Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
• Long-time dynamics in quantum spin lattices: ergodicity and hydrodynamic projections at all frequencies and wavelengths
• Quasiparticle Picture for Entanglement Hamiltonians in Higher Dimensions
• Wigner dynamics for quantum gases under inhomogeneous gain and loss processes with dephasing
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• High-low pressure domain wall for the classical Toda lattice
• Universal Counterdiabatic Driving
• Thermalization and hydrodynamics in an interacting integrable system: the case of hard rods
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Soliton gas of the integrable Boussinesq equation and its generalised hydrodynamics
• Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders
• Subdiffusive transport in the Fredkin dynamical universality class
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• On two reversible cellular automata with two particle species
• Exceptional stationary state in a dephasing many-body open quantum system
• The Staircase Model: Massless Flows and Hydrodynamics
• Single-file dynamics with general charge measures
• Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation
• Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
• Hamiltonian formulation and aspects of integrability of generalised hydrodynamics
• Quantum feedback induced entanglement relaxation and dynamical phase transition in monitored free fermion chains with Wannier-Stark ladder
• Dynamical separation of charge and energy transport in one-dimensional Mott insulators
• Viscous Flow in a 1D Spin-Polarized Fermi Gas: the Role of Integrability on Viscosity
• Phase space holography with no strings attached
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• Experimental Investigation of a Bipartite Quench in a 1D Bose gas
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Quench dynamics of entanglement entropy under projective charge measurements: the free fermion case
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
• Emergence of generalized hydrodynamics in the non-local Luttinger model
• Diffusive hydrodynamics of hard rods from microscopics
• Simulating generalised fluids via interacting wave packets evolution
• Generalized hydrodynamics in complete box-ball system for $U_q({\widehat{sl}}_n)$
• Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• Kinetics of Quantum Reaction-Diffusion systems
• Dynamics of Interaction of Two Soliton Clouds
• Wavelet representation of hardcore bosons
• Conserved densities of hard rods: microscopic to hydrodynamic solutions
• Reaction-diffusion dynamics of the weakly dissipative Fermi gas
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Hydrodynamic fluctuations of stochastic charged cellular automata
• A hydrodynamic approach to Stark localization
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Tails of Instability and Decay: a Hydrodynamic Perspective
• One-body correlations and momentum distributions of trapped one-dimensional Bose gases at finite temperature
• Domain-wall melting and entanglement in free-fermion chains with a band structure
• Hydrodynamic non-linear response of interacting integrable systems
• Relaxation and fluctuations of a mass- and dipole-conserving stochastic lattice gas
• Microscopic and hydrodynamic correlation in 1d hard rod gas
• Timescales and necessary conditions for hydrodynamization in one-dimensional Bose gases
• Full counting statistics after quantum quenches as hydrodynamic fluctuations
• Universal thermalization dynamics in (1+1)d QFTs
• Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise
• Generalized Hydrodynamics for the Volterra lattice: Ballistic and nonballistic behavior of correlation functions
• Generalized Gibbs Ensemble from Eigenstate Entanglement Hamiltonian
• Time Evolution of the Symmetry Resolved Entanglement Entropy after a Mass Quench
• Entanglement dynamics of a hard-core quantum gas during a Joule expansion
• Generalised Gibbs Ensemble for spherically constrained harmonic models
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model
• Rationally independent free fermions with local hopping
• Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas
• Boundary-driven magnetization transport in the spin-$1/2$ XXZ chain: Role of the system-bath coupling strength and timescales
• Particle-hole origin of thermal beating in dipole-compression modes of a 1D Bose gas
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description
• Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits
• Integral formula for the propagator of the one-dimensional Hubbard model
• Lax random matrices from Calogero systems