SciPost Physics

Equations of state in generalized hydrodynamics

Dinh-Long Vu, Takato Yoshimura

SciPost Phys. 6, 023 (2019) · published 15 February 2019

• doi: 10.21468/SciPostPhys.6.2.023
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Abstract

We, for the first time, report a first-principle proof of the equations of state used in the hydrodynamic theory for integrable systems, termed generalized hydrodynamics (GHD). The proof makes full use of the graph theoretic approach to Thermodynamic Bethe ansatz (TBA) that was proposed recently. This approach is purely combinatorial and relies only on common structures shared among Bethe solvable models, suggesting universal applicability of the method. To illustrate the idea of the proof, we focus on relativistic integrable quantum field theories with diagonal scatterings and without bound states such as strings.

• Bertini et al., Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics
  Phys. Rev. B 100, 035108 (2019) [Crossref]
• Bajnok et al., Exact finite volume expectation values of conserved currents
  Physics Letters B 805, 135446 135446 (2020) [Crossref]
• Ruggiero et al., Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
  SciPost Phys. 6, 051 (2019) [Crossref]
• Fagotti, Locally quasi-stationary states in noninteracting spin chains
  SciPost Phys. 8, 048 (2020) [Crossref]
• Møller et al., Euler-scale dynamical correlations in integrable systems with fluid motion
  SciPost Phys. Core 3, 016 (2020) [Crossref]
• Moosavi, Emergence of generalized hydrodynamics in the non-local Luttinger model
  SciPost Phys. 9, 037 (2020) [Crossref]
• Medenjak et al., Thermal transport in TT¯ -deformed conformal field theories: From integrability to holography
  Phys. Rev. D 103, 066012 (2021) [Crossref]
• Jiang, $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
  SciPost Phys. 12, 191 (2022) [Crossref]
• Ruggiero et al., Quantum Generalized Hydrodynamics
  Phys. Rev. Lett. 124, 140603 (2020) [Crossref]
• El et al., Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation
  Phys. Rev. E 101, 052207 (2020) [Crossref]
• Mistakidis et al., Few-body Bose gases in low dimensions—A laboratory for quantum dynamics
  Physics Reports 1042, 1 (2023) [Crossref]
• Scopa et al., Generalized hydrodynamics of the repulsive spin- 12 Fermi gas
  Phys. Rev. B 106, 134314 (2022) [Crossref]
• Bertini et al., Finite-temperature transport in one-dimensional quantum lattice models
  Rev. Mod. Phys. 93, 025003 (2021) [Crossref]
• Spohn, Collision rate ansatz for the classical Toda lattice
  Phys. Rev. E 101, 060103 (2020) [Crossref]
• Pozsgay, Current operators in integrable spin chains: lessons from long range deformations
  SciPost Phys. 8, 016 (2020) [Crossref]
• Perfetto et al., Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
  SciPost Phys. 10, 116 (2021) [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]
• Doyon et al., The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
  SciPost Phys. 13, 072 (2022) [Crossref]
• De Nardis et al., Diffusion in generalized hydrodynamics and quasiparticle scattering
  SciPost Phys. 6, 049 (2019) [Crossref]
• Mazzoni et al., The staircase model: massless flows and hydrodynamics
  J. Phys. A: Math. Theor. 54, 404005 (2021) [Crossref]
• Doyon, Lecture notes on Generalised Hydrodynamics
  SciPost Phys. Lect. Notes, 18 (2020) [Crossref]
• Malvania et al., Generalized hydrodynamics in strongly interacting 1D Bose gases
  Science 373, 1129 (2021) [Crossref]
• Borsi et al., Current Operators in Bethe Ansatz and Generalized Hydrodynamics: An Exact Quantum-Classical Correspondence
  Phys. Rev. X 10, 011054 (2020) [Crossref]
• Suret et al., Nonlinear Spectral Synthesis of Soliton Gas in Deep-Water Surface Gravity Waves
  Phys. Rev. Lett. 125, 264101 (2020) [Crossref]
• Alba et al., Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects
  J. Stat. Mech. 2021, 114004 (2021) [Crossref]
• Mestyán et al., Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
  SciPost Phys. 8, 055 (2020) [Crossref]
• Jiang et al., Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function
  J. High Energ. Phys. 2020, 37 (2020) [Crossref]
• Kostov, Effective Quantum Field Theory for the Thermodynamical Bethe Ansatz
  J. High Energ. Phys. 2020, 43 (2020) [Crossref]
• Cubero et al., Form factors and generalized hydrodynamics for integrable systems
  J. Stat. Mech. 2021, 114002 (2021) [Crossref]
• Vu, Cumulants of conserved charges in GGE and cumulants of total transport in GHD: exact summation of matrix elements?
  J. Stat. Mech. 2020, 023103 (2020) [Crossref]
• Pozsgay, Algebraic Construction of Current Operators in Integrable Spin Chains
  Phys. Rev. Lett. 125, 070602 (2020) [Crossref]
• Congy et al., Soliton gas in bidirectional dispersive hydrodynamics
  Phys. Rev. E 103, 042201 (2021) [Crossref]
• Horváth, Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem
  J. High Energ. Phys. 2019, 20 (2019) [Crossref]
• Collura et al., Domain wall melting in the spin- 12 XXZ spin chain: Emergent Luttinger liquid with a fractal quasiparticle charge
  Phys. Rev. B 102, 180409 (2020) [Crossref]
• Kuijlaars et al., On minimal energy solutions to certain classes of integral equations related to soliton gases for integrable systems*
  Nonlinearity 34, 7227 (2021) [Crossref]
• Borsi et al., Current operators in integrable models: a review
  J. Stat. Mech. 2021, 094001 (2021) [Crossref]
• Tovbis et al., Recent developments in spectral theory of the focusing NLS soliton and breather gases: the thermodynamic limit of average densities, fluxes and certain meromorphic differentials; periodic gases
  J. Phys. A: Math. Theor. 55, 424006 (2022) [Crossref]
• Kerr et al., The theory of generalised hydrodynamics for the one-dimensional Bose gas
  AAPPS Bull. 33, 25 (2023) [Crossref]
• Myers et al., Transport fluctuations in integrable models out of equilibrium
  SciPost Phys. 8, 007 (2020) [Crossref]
• Bettelheim, The Whitham approach to the c → 0 limit of the Lieb–Liniger model and generalized hydrodynamics
  J. Phys. A: Math. Theor. 53, 205204 (2020) [Crossref]
• Yoshimura et al., Collision rate ansatz for quantum integrable systems
  SciPost Phys. 9, 040 (2020) [Crossref]
• Bouchoule et al., Generalized hydrodynamics in the one-dimensional Bose gas: theory and experiments
  J. Stat. Mech. 2022, 014003 (2022) [Crossref]
• Szász-Schagrin et al., Weak integrability breaking and level spacing distribution
  SciPost Phys. 11, 037 (2021) [Crossref]