SciPost Physics Core

Linearized regime of the generalized hydrodynamics with diffusion

Miłosz Panfil, Jacek Pawełczyk

SciPost Phys. Core 1, 002 (2019) · published 22 November 2019

• doi: 10.21468/SciPostPhysCore.1.1.002
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Abstract

We consider the generalized hydrodynamics including the recently introduced diffusion term for an initially inhomogeneous state in the Lieb-Liniger model. We construct a general solution to the linearized hydrodynamics equation in terms of the eigenstates of the evolution operator and study two prototypical classes of initial states: delocalized and localized spatially. We exhibit some general features of the resulting dynamics, among them, we highlight the difference between the ballistic and diffusive evolution. The first one governs a spatial scrambling, the second, a scrambling of the quasi-particles content. We also go one step beyond the linear regime and discuss the evolution of the zero momentum mode that does not evolve in the linear regime.

• Watson et al., Benchmarks of generalized hydrodynamics for one-dimensional Bose gases
  Phys. Rev. Research 5, L022024 (2023) [Crossref]
• Bouchoule et al., Generalized hydrodynamics in the one-dimensional Bose gas: theory and experiments
  J. Stat. Mech. 2022, 014003 (2022) [Crossref]
• Ruggiero et al., Quantum Generalized Hydrodynamics
  Phys. Rev. Lett. 124, 140603 (2020) [Crossref]
• Panfil et al., Thermalization of Interacting Quasi-One-Dimensional Systems
  Phys. Rev. Lett. 130, 030401 (2023) [Crossref]
• Bastianello et al., Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion
  Phys. Rev. Lett. 125, 240604 (2020) [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]
• De Nardis et al., Correlation functions and transport coefficients in generalised hydrodynamics
  J. Stat. Mech. 2022, 014002 (2022) [Crossref]
• Panfil, The two particle–hole pairs contribution to the dynamic correlation functions of quantum integrable models
  J. Stat. Mech. 2021, 013108 (2021) [Crossref]
• Medenjak et al., Diffusion from convection
  SciPost Phys. 9, 075 (2020) [Crossref]
• Rylands et al., Many-Body Dynamical Localization in a Kicked Lieb-Liniger Gas
  Phys. Rev. Lett. 124, 155302 (2020) [Crossref]
• Cataldini et al., Emergent Pauli Blocking in a Weakly Interacting Bose Gas
  Phys. Rev. X 12, 041032 (2022) [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]
• Perfetto et al., Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
  SciPost Phys. 10, 116 (2021) [Crossref]
• Cortes Cubero et al., Generalized hydrodynamics regime from the thermodynamic bootstrap program
  SciPost Phys. 8, 004 (2020) [Crossref]