SciPost Physics Lecture Notes

SciPost Phys. Lect. Notes 18 (2020) · published 28 August 2020

Part of the 2018-08: Integrability in Atomic and Condensed Matter Physics Collection in the Les Houches Summer School Lecture Notes Series.

• doi: 10.21468/SciPostPhysLectNotes.18
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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.

• Panfil et al., Thermalization of Interacting Quasi-One-Dimensional Systems
  Phys. Rev. Lett. 130, 030401 (2023) [Crossref]
• Kuniba et al., Generalized hydrodynamics in complete box-ball system for $U_q(\widehat{sl}_n)$
  SciPost Phys. 10, 095 (2021) [Crossref]
• Kamchatnov et al., Dynamics of Interaction between Two Soliton Clouds
  J. Exp. Theor. Phys. 135, 768 (2022) [Crossref]
• Nagy et al., Thermodynamics and fractal Drude weights in the sine-Gordon model
  Phys. Rev. B 108, L241105 (2023) [Crossref]
• Malvania et al., Generalized hydrodynamics in strongly interacting 1D Bose gases
  Science 373, 1129 (2021) [Crossref]
• Ecker et al., Non-equilibrium steady state formation in 3+1 dimensions
  SciPost Phys. 11, 047 (2021) [Crossref]
• Bulchandani et al., Superdiffusion in spin chains
  J. Stat. Mech. 2021, 084001 (2021) [Crossref]
• Perfetto et al., Dynamics of large deviations in the hydrodynamic limit: Noninteracting systems
  Phys. Rev. E 102, 042128 (2020) [Crossref]
• Scopa et al., One-particle density matrix and momentum distribution of the out-of-equilibrium one-dimensional Tonks-Girardeau gas: Analytical results at large N
  Phys. Rev. A 108, 013324 (2023) [Crossref]
• El, Soliton gas in integrable dispersive hydrodynamics
  J. Stat. Mech. 2021, 114001 (2021) [Crossref]
• Mazzuca et al., Large deviations for Ablowitz-Ladik lattice, and the Schur flow
  Electron. J. Probab. 28, (2023) [Crossref]
• Scopa et al., Generalized hydrodynamics of the repulsive spin- 12 Fermi gas
  Phys. Rev. B 106, 134314 (2022) [Crossref]
• Bonnemain et al., Generalized hydrodynamics of the KdV soliton gas
  J. Phys. A: Math. Theor. 55, 374004 (2022) [Crossref]
• Ares et al., Entanglement dynamics of a hard-core quantum gas during a Joule expansion
  J. Phys. A: Math. Theor. 55, 375301 (2022) [Crossref]
• Hübner, Mesoscopic impurities in generalized hydrodynamics
  J. Stat. Mech. 2024, 033102 (2024) [Crossref]
• Coppola et al., Growth of entanglement entropy under local projective measurements
  Phys. Rev. B 105, 094303 (2022) [Crossref]
• Kulagin et al., Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation
  Phys. Scr. 99, 045228 (2024) [Crossref]
• Ampelogiannis et al., Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths
  Ann. Henri Poincaré 25, 65 (2024) [Crossref]
• Doyon et al., The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
  SciPost Phys. 13, 072 (2022) [Crossref]
• Morningstar et al., Hydrodynamics in long-range interacting systems with center-of-mass conservation
  Phys. Rev. B 108, L020304 (2023) [Crossref]
• Bastianello et al., Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion
  Phys. Rev. Lett. 125, 240604 (2020) [Crossref]
• Lopez-Piqueres et al., Integrability breaking in the Rule 54 cellular automaton
  J. Phys. A: Math. Theor. 55, 234005 (2022) [Crossref]
• Wei et al., Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
  Science 376, 716 (2022) [Crossref]
• Calabrese, Entanglement spreading in non-equilibrium integrable systems
  SciPost Phys. Lect. Notes, 20 (2020) [Crossref]
• Suret et al., Soliton refraction by an optical soliton gas
  Phys. Rev. Research 5, L042002 (2023) [Crossref]
• Jonay et al., Slow thermalization and subdiffusion in U(1) conserving Floquet random circuits
  Phys. Rev. B 109, 024311 (2024) [Crossref]
• Heitmann et al., Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
  Phys. Rev. Research 4, 043147 (2022) [Crossref]
• Klobas et al., On two reversible cellular automata with two particle species
  J. Phys. A: Math. Theor. 55, 094003 (2022) [Crossref]
• Barbier et al., Generalised Gibbs Ensemble for spherically constrained harmonic models
  SciPost Phys. 13, 048 (2022) [Crossref]
• Coppola et al., Wigner dynamics for quantum gases under inhomogeneous gain and loss processes with dephasing
  Phys. Rev. A 107, 052213 (2023) [Crossref]
• Kos et al., Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
  Phys. Rev. X 11, 011022 (2021) [Crossref]
• Doyon et al., Emergence of Hydrodynamic Spatial Long-Range Correlations in Nonequilibrium Many-Body Systems
  Phys. Rev. Lett. 131, 027101 (2023) [Crossref]
• Capizzi et al., A hydrodynamic approach to Stark localization
  J. Stat. Mech. 2023, 073104 (2023) [Crossref]
• Mistakidis et al., Few-body Bose gases in low dimensions—A laboratory for quantum dynamics
  Physics Reports 1042, 1 (2023) [Crossref]
• Durnin et al., Nonequilibrium Dynamics and Weakly Broken Integrability
  Phys. Rev. Lett. 127, 130601 (2021) [Crossref]
• Vergallo et al., Hamiltonian systems of Jordan block type: Delta-functional reductions of the kinetic equation for soliton gas
  64, 103505 (2023) [Crossref]
• Ae et al., Spin Drude weight for the integrable XXZ chain with arbitrary spin
  J. Stat. Mech. 2024, 033104 (2024) [Crossref]
• De Nardis et al., Stability of Superdiffusion in Nearly Integrable Spin Chains
  Phys. Rev. Lett. 127, 057201 (2021) [Crossref]
• Maki et al., Viscous flow in a one-dimensional spin-polarized Fermi gas: The role of integrability on viscosity
  Phys. Rev. A 107, 013310 (2023) [Crossref]
• McRoberts et al., Anomalous dynamics and equilibration in the classical Heisenberg chain
  Phys. Rev. B 105, L100403 (2022) [Crossref]
• Alba et al., Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects
  J. Stat. Mech. 2021, 114004 (2021) [Crossref]
• Rylands et al., Solution of the BEC to BCS Quench in One Dimension
  Phys. Rev. Lett. 130, 023001 (2023) [Crossref]
• Bertini et al., Finite-temperature transport in one-dimensional quantum lattice models
  Rev. Mod. Phys. 93, 025003 (2021) [Crossref]
• Riggio et al., Effects of atom losses on a one-dimensional lattice gas of hard-core bosons
  Phys. Rev. A 109, 023311 (2024) [Crossref]
• Fujimoto et al., Random Matrix Statistics in Propagating Correlation Fronts of Fermions
  Phys. Rev. Lett. 132, 087101 (2024) [Crossref]
• Scopa et al., Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
  SciPost Phys. 12, 207 (2022) [Crossref]
• del Vecchio del Vecchio et al., Entanglement Rényi entropies from ballistic fluctuation theory: The free fermionic case
  SciPost Phys. Core 7, 005 (2024) [Crossref]
• Kerr et al., The theory of generalised hydrodynamics for the one-dimensional Bose gas
  AAPPS Bull. 33, 25 (2023) [Crossref]
• Copie et al., Space–time observation of the dynamics of soliton collisions in a recirculating optical fiber loop
  Optics Communications 545, 129647 129647 (2023) [Crossref]
• Grava et al., Generalized Gibbs Ensemble of the Ablowitz–Ladik Lattice, Circular $$\beta $$-Ensemble and Double Confluent Heun Equation
  Commun. Math. Phys. 399, 1689 (2023) [Crossref]
• Klobas et al., Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
  SciPost Phys. 11, 106 (2021) [Crossref]
• Mendl et al., High-low pressure domain wall for the classical Toda lattice
  SciPost Phys. Core 5, 002 (2022) [Crossref]
• Balducci et al., Interface dynamics in the two-dimensional quantum Ising model
  Phys. Rev. B 107, 024306 (2023) [Crossref]
• De Nardis et al., Correlation functions and transport coefficients in generalised hydrodynamics
  J. Stat. Mech. 2022, 014002 (2022) [Crossref]
• Kuniba et al., Current correlations, Drude weights and large deviations in a box–ball system
  J. Phys. A: Math. Theor. 55, 244006 (2022) [Crossref]
• Kethepalli et al., Finite-temperature equilibrium density profiles of integrable systems in confining potentials
  Phys. Rev. E 107, 044101 (2023) [Crossref]
• Møller et al., Whitham approach to Generalized Hydrodynamics
  Phys. Rev. Research 6, 013328 (2024) [Crossref]
• Granet, Wavelet representation of hardcore bosons
  J. Stat. Mech. 2023, 123102 (2023) [Crossref]
• Del Vecchio Del Vecchio et al., The hydrodynamic theory of dynamical correlation functions in the XX chain
  J. Stat. Mech. 2022, 053102 (2022) [Crossref]
• Sala et al., Dynamics in Systems with Modulated Symmetries
  Phys. Rev. Lett. 129, 170601 (2022) [Crossref]
• McRoberts et al., Long-lived solitons and their signatures in the classical Heisenberg chain
  Phys. Rev. E 106, L062202 (2022) [Crossref]
• Mazzoni et al., The staircase model: massless flows and hydrodynamics
  J. Phys. A: Math. Theor. 54, 404005 (2021) [Crossref]
• Doyon et al., Ballistic macroscopic fluctuation theory
  SciPost Phys. 15, 136 (2023) [Crossref]
• Kormos et al., Finite-temperature dynamics in gapped one-dimensional models in the sine-Gordon family
  Phys. Rev. B 106, 205151 (2022) [Crossref]
• Perfetto et al., Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
  SciPost Phys. 10, 116 (2021) [Crossref]
• Lopez-Piqueres et al., Operator front broadening in chaotic and integrable quantum chains
  Phys. Rev. B 104, 104307 (2021) [Crossref]
• Ishiguro et al., Asymmetry-induced delocalization transition in the integrable non-Hermitian spin chain
  Phys. Rev. Research 5, 033102 (2023) [Crossref]
• Ilievski, Popcorn Drude weights from quantum symmetry
  J. Phys. A: Math. Theor. 55, 504005 (2022) [Crossref]
• Moosavi, Emergence of generalized hydrodynamics in the non-local Luttinger model
  SciPost Phys. 9, 037 (2020) [Crossref]
• Tartaglia et al., Real-time evolution in the Hubbard model with infinite repulsion
  SciPost Phys. 12, 028 (2022) [Crossref]
• Dóra et al., Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description
  Phys. Rev. B 108, L121105 (2023) [Crossref]
• Scopa et al., Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
  J. Phys. A: Math. Theor. 54, 404002 (2021) [Crossref]
• Krajnik et al., Absence of Normal Fluctuations in an Integrable Magnet
  Phys. Rev. Lett. 128, 090604 (2022) [Crossref]
• Bastianello et al., Hydrodynamics of weak integrability breaking
  J. Stat. Mech. 2021, 114003 (2021) [Crossref]
• Congy et al., Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation
  J Nonlinear Sci 33, 104 (2023) [Crossref]
• Castro-Alvaredo et al., Tails of Instability and Decay: a Hydrodynamic Perspective
  SciPost Phys. 12, 115 (2022) [Crossref]
• Ilievski et al., Superuniversality of Superdiffusion
  Phys. Rev. X 11, 031023 (2021) [Crossref]
• Krajnik et al., Anisotropic Landau-Lifshitz model in discrete space-time
  SciPost Phys. 11, 051 (2021) [Crossref]
• Spohn, Hydrodynamic equations for the Ablowitz–Ladik discretization of the nonlinear Schrödinger equation
  63, 033305 (2022) [Crossref]
• Bertini et al., Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
  Phys. Rev. Lett. 131, 140401 (2023) [Crossref]
• Del Vecchio et al., Exact Large-Scale Fluctuations of the Phase Field in the Sine-Gordon Model
  Phys. Rev. Lett. 131, 263401 (2023) [Crossref]
• Le et al., Observation of hydrodynamization and local prethermalization in 1D Bose gases
  Nature 618, 494 (2023) [Crossref]
• Moosavi, Inhomogeneous Conformal Field Theory Out of Equilibrium
  Ann. Henri Poincaré 25, 1083 (2024) [Crossref]
• Bernard, Can the macroscopic fluctuation theory be quantized?
  J. Phys. A: Math. Theor. 54, 433001 (2021) [Crossref]
• Nussinov, Reduced probability densities of long-lived metastable states as those of distributed thermal systems: Possible experimental implications for supercooled fluids
  Annals of Physics 463, 169634 169634 (2024) [Crossref]
• Feldmeier et al., Anomalous Diffusion in Dipole- and Higher-Moment-Conserving Systems
  Phys. Rev. Lett. 125, 245303 (2020) [Crossref]
• Jiang, $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
  SciPost Phys. 12, 191 (2022) [Crossref]
• Scopa et al., Scaling of fronts and entanglement spreading during a domain wall melting
  Eur. Phys. J. Spec. Top. 232, 1763 (2023) [Crossref]
• Hruza et al., Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP, and Free Probability
  Phys. Rev. X 13, 011045 (2023) [Crossref]
• Essler, A short introduction to Generalized Hydrodynamics
  Physica A: Statistical Mechanics and its Applications 631, 127572 127572 (2023) [Crossref]
• Lopez-Piqueres et al., Hydrodynamics of nonintegrable systems from a relaxation-time approximation
  Phys. Rev. B 103, L060302 (2021) [Crossref]
• Horváth et al., Full counting statistics of charge in quenched quantum gases
  Phys. Rev. A 109, 043302 (2024) [Crossref]
• Cecile et al., Squeezed Ensembles and Anomalous Dynamic Roughening in Interacting Integrable Chains
  Phys. Rev. Lett. 132, 130401 (2024) [Crossref]
• Medenjak et al., Thermal transport in TT¯ -deformed conformal field theories: From integrability to holography
  Phys. Rev. D 103, 066012 (2021) [Crossref]
• Doyon, Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems
  Commun. Math. Phys. 391, 293 (2022) [Crossref]
• Zadnik et al., The folded spin-1/2 XXZ model: II. Thermodynamics and hydrodynamics with a minimal set of charges
  SciPost Phys. 10, 099 (2021) [Crossref]
• Roósz, Front dynamics in the Harper model
  Phys. Rev. B 109, 064204 (2024) [Crossref]
• Watson et al., Benchmarks of generalized hydrodynamics for one-dimensional Bose gases
  Phys. Rev. Research 5, L022024 (2023) [Crossref]
• Fava et al., Hydrodynamic nonlinear response of interacting integrable systems
  Proc. Natl. Acad. Sci. U.S.A. 118, e2106945118 (2021) [Crossref]
• De Nardis et al., Nonlinear Fluctuating Hydrodynamics for Kardar-Parisi-Zhang Scaling in Isotropic Spin Chains
  Phys. Rev. Lett. 131, 197102 (2023) [Crossref]
• Khveshchenko, Phase space holography with no strings attached
  physics 61, (2022) [Crossref]
• Gopalakrishnan et al., Anomalous transport from hot quasiparticles in interacting spin chains
  Rep. Prog. Phys. 86, 036502 (2023) [Crossref]
• Cubero et al., Form factors and generalized hydrodynamics for integrable systems
  J. Stat. Mech. 2021, 114002 (2021) [Crossref]
• Møller et al., Euler-scale dynamical correlations in integrable systems with fluid motion
  SciPost Phys. Core 3, 016 (2020) [Crossref]
• Fisher et al., Random Quantum Circuits
  Annu. Rev. Condens. Matter Phys. 14, 335 (2023) [Crossref]