SciPost Physics

A note on generalized hydrodynamics: inhomogeneous fields and other concepts

Benjamin Doyon, Takato Yoshimura

SciPost Phys. 2, 014 (2017) · published 22 April 2017

• doi: 10.21468/SciPostPhys.2.2.014
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Abstract

Generalized hydrodynamics (GHD) was proposed recently as a formulation of hydrodynamics for integrable systems, taking into account infinitely-many conservation laws. In this note we further develop the theory in various directions. By extending GHD to all commuting flows of the integrable model, we provide a full description of how to take into account weakly varying force fields, temperature fields and other inhomogeneous external fields within GHD. We expect this can be used, for instance, to characterize the non-equilibrium dynamics of one-dimensional Bose gases in trap potentials. We further show how the equations of state at the core of GHD follow from the continuity relation for entropy, and we show how to recover Euler-like equations and discuss possible viscosity terms.

• Jacopo De Nardis et al., Hydrodynamic Diffusion in Integrable Systems
  Phys. Rev. Lett. 121, 160603 (2018) [Crossref]
• Juris Reisons et al., Emergent transport in a many-body open system driven by interacting quantum baths
  Phys. Rev. B 96, 165137 (2017) [Crossref]
• D. X. Horváth, Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem
  J. High Energ. Phys. 2019, 20 (2019) [Crossref]
• Vincenzo Alba et al., Entanglement dynamics after quantum quenches in generic integrable systems
  SciPost Phys. 4, 017 (2018) [Crossref]
• Bruno Bertini et al., Universal Broadening of the Light Cone in Low-Temperature Transport
  Phys. Rev. Lett. 120, 176801 (2018) [Crossref]
• Benjamin Doyon, Exact large-scale correlations in integrable systems out of equilibrium
  SciPost Phys. 5, 054 (2018) [Crossref]
• Vir B. Bulchandani et al., Subdiffusive front scaling in interacting integrable models
  Phys. Rev. B 99, 121410 (2019) [Crossref]
• Jacopo De Nardis et al., Edge Singularities and Quasilong-Range Order in Nonequilibrium Steady States
  Phys. Rev. Lett. 120, 217206 (2018) [Crossref]
• Márton Mestyán et al., Spin-charge separation effects in the low-temperature transport of one-dimensional Fermi gases
  Phys. Rev. B 99, 014305 (2019) [Crossref]
• Bruno Bertini et al., Low-temperature transport in out-of-equilibrium XXZ chains
  J. Stat. Mech. 2018, 033104 (2018) [Crossref]
• Lorenzo Piroli et al., Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions
  Phys. Rev. B 96, 115124 (2017) [Crossref]
• Krzysztof Gawędzki et al., Finite-Time Universality in Nonequilibrium CFT
  J Stat Phys 172, 353 (2018) [Crossref]
• Alvise Bastianello et al., Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model
  SciPost Phys. 4, 045 (2018) [Crossref]
• Sarang Gopalakrishnan et al., Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
  Phys. Rev. B 98, 220303 (2018) [Crossref]
• M. Schemmer et al., Generalized Hydrodynamics on an Atom Chip
  Phys. Rev. Lett. 122, 090601 (2019) [Crossref]
• Paola Ruggiero et al., Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
  SciPost Phys. 6, 051 (2019) [Crossref]
• Benjamin Doyon et al., Soliton Gases and Generalized Hydrodynamics
  Phys. Rev. Lett. 120, 045301 (2018) [Crossref]
• Benjamin Doyon et al., A geometric viewpoint on generalized hydrodynamics
  Nuclear Physics B 926, 570 (2018) [Crossref]
• Benjamin Doyon et al., Drude Weight for the Lieb-Liniger Bose Gas
  SciPost Phys. 3, 039 (2017) [Crossref]
• Márton Kormos, Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
  SciPost Phys. 3, 020 (2017) [Crossref]
• Bruno Bertini et al., Quantum quench in the infinitely repulsive Hubbard model: the stationary state
  J. Stat. Mech. 2017, 103107 (2017) [Crossref]
• Alvise Bastianello et al., From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
  J. Stat. Mech. 2018, 113104 (2018) [Crossref]
• Bruno Bertini et al., Entanglement evolution and generalised hydrodynamics: noninteracting systems
  J. Phys. A: Math. Theor. 51, 39LT01 (2018) [Crossref]
• Jean-Sébastien Caux et al., Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup
  SciPost Phys. 6, 070 (2019) [Crossref]
• Vincenzo Alba et al., Entanglement evolution and generalised hydrodynamics: interacting integrable systems
  SciPost Phys. 7, 005 (2019) [Crossref]
• Benjamin Doyon et al., Fluctuations in Ballistic Transport from Euler Hydrodynamics
  Ann. Henri Poincaré, (2019) [Crossref]
• Jacopo De Nardis et al., Diffusion in generalized hydrodynamics and quasiparticle scattering
  SciPost Phys. 6, 049 (2019) [Crossref]
• Xiangyu Cao et al., Incomplete Thermalization from Trap-Induced Integrability Breaking: Lessons from Classical Hard Rods
  Phys. Rev. Lett. 120, 164101 (2018) [Crossref]
• Sarang Gopalakrishnan et al., Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains
  Phys. Rev. Lett. 122, 127202 (2019) [Crossref]
• Matthias Gruber et al., Magnetization and entanglement after a geometric quench in the XXZ chain
  Phys. Rev. B 99, 174403 (2019) [Crossref]
• Vir B. Bulchandani et al., Solvable Hydrodynamics of Quantum Integrable Systems
  Phys. Rev. Lett. 119, 220604 (2017) [Crossref]
• Benjamin Doyon, Generalized hydrodynamics of the classical Toda system
  Journal of Mathematical Physics 60, 073302 (2019) [Crossref]
• J. M. Maillet et al., On quantum separation of variables
  Journal of Mathematical Physics 59, 091417 (2018) [Crossref]
• Alvise Bastianello, Lack of thermalization for integrability-breaking impurities
  EPL 125, 20001 (2019) [Crossref]
• Dinh-Long VU et al., Equations of state in generalized hydrodynamics
  SciPost Phys. 6, 023 (2019) [Crossref]
• Jacopo De Nardis et al., Anomalous Spin Diffusion in One-Dimensional Antiferromagnets
  Phys. Rev. Lett. 123, 186601 (2019) [Crossref]
• Alvise Bastianello et al., Spreading of entanglement and correlations after a quench with intertwined quasiparticles
  SciPost Phys. 5, 033 (2018) [Crossref]
• Alvise Bastianello et al., Nonequilibrium Steady State Generated by a Moving Defect: The Supersonic Threshold
  Phys. Rev. Lett. 120, 060602 (2018) [Crossref]
• Enej Ilievski et al., Ballistic transport in the one-dimensional Hubbard model: The hydrodynamic approach
  Phys. Rev. B 96, 081118 (2017) [Crossref]
• Mario Collura et al., Analytic solution of the domain-wall nonequilibrium stationary state
  Phys. Rev. B 97, 081111 (2018) [Crossref]
• Enej Ilievski et al., Superdiffusion in One-Dimensional Quantum Lattice Models
  Phys. Rev. Lett. 121, 230602 (2018) [Crossref]
• J De Nardis et al., Particle-hole pairs and density–density correlations in the Lieb–Liniger model
  J. Stat. Mech. 2018, 033102 (2018) [Crossref]
• Vincenzo Alba, Towards a generalized hydrodynamics description of Rényi entropies in integrable systems
  Phys. Rev. B 99, 045150 (2019) [Crossref]
• Alvise Bastianello et al., Superluminal moving defects in the Ising spin chain
  Phys. Rev. B 98, 064304 (2018) [Crossref]
• Alvise Bastianello et al., Integrability-Protected Adiabatic Reversibility in Quantum Spin Chains
  Phys. Rev. Lett. 122, 240606 (2019) [Crossref]
• Maurizio Fagotti, Higher-order generalized hydrodynamics in one dimension: The noninteracting test
  Phys. Rev. B 96, 220302 (2017) [Crossref]
• Vir B. Bulchandani et al., Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain
  Phys. Rev. B 97, 045407 (2018) [Crossref]
• Vincenzo Alba, Entanglement and quantum transport in integrable systems
  Phys. Rev. B 97, 245135 (2018) [Crossref]
• Utkarsh Agrawal et al., Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
  Phys. Rev. B 99, 174203 (2019) [Crossref]
• Aaron J. Friedman et al., Integrable Many-Body Quantum Floquet-Thouless Pumps
  Phys. Rev. Lett. 123, 170603 (2019) [Crossref]
• Manas Kulkarni et al., Quantum quench and thermalization of one-dimensional Fermi gas via phase-space hydrodynamics
  Phys. Rev. A 98, 043610 (2018) [Crossref]
• Márton Kormos et al., Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench
  Phys. Rev. E 98, 032105 (2018) [Crossref]
• Alvise Bastianello et al., Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions
  Phys. Rev. Lett. 123, 130602 (2019) [Crossref]
• Leonardo Mazza et al., Energy transport in an integrable parafermionic chain via generalized hydrodynamics
  Phys. Rev. B 98, 075421 (2018) [Crossref]
• Sarang Gopalakrishnan et al., Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
  Proc Natl Acad Sci USA 116, 16250 (2019) [Crossref]
• Viktor Eisler et al., Front dynamics and entanglement in the XXZ chain with a gradient
  Phys. Rev. B 96, 174301 (2017) [Crossref]
• Benjamin Doyon et al., Dynamics of hard rods with initial domain wall state
  J. Stat. Mech. 2017, 073210 (2017) [Crossref]