SciPost Physics

SciPost Phys. 9, 075 (2020) · published 19 November 2020

• doi: 10.21468/SciPostPhys.9.5.075
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

We introduce non-trivial contributions to diffusion constant in generic many-body systems arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in the vicinity of equilibrium states in terms of powers of local and quasi-local conserved quantities. We show that only the second-order terms in this expansion carry a finite contribution to diffusive spreading. Our formalism implies that whenever there are at least two coupled modes with degenerate group velocities, the system behaves super-diffusively, in accordance with the non-linear fluctuating hydrodynamics theory. Finally, we show that our expression saturates the exact diffusion constants in quantum and classical interacting integrable systems, providing a general framework to derive these expressions.

• Scopa et al., Generalized hydrodynamics of the repulsive spin- 12 Fermi gas
  Phys. Rev. B 106, 134314 (2022) [Crossref]
• De Nardis et al., Hydrodynamic gauge fixing and higher order hydrodynamic expansion
  J. Phys. A: Math. Theor. 56, 245001 (2023) [Crossref]
• Capizzi et al., A hydrodynamic approach to Stark localization
  J. Stat. Mech. 2023, 073104 (2023) [Crossref]
• Urichuk et al., Navier-Stokes Equations for Low-Temperature One-Dimensional Quantum Fluids
  Phys. Rev. Lett. 132, 243402 (2024) [Crossref]
• Doyon, Diffusion and Superdiffusion from Hydrodynamic Projections
  J Stat Phys 186, 25 (2022) [Crossref]
• Medenjak et al., Thermal transport in TT¯ -deformed conformal field theories: From integrability to holography
  Phys. Rev. D 103, 066012 (2021) [Crossref]
• Gopalakrishnan et al., Anomalous transport from hot quasiparticles in interacting spin chains
  Rep. Prog. Phys. 86, 036502 (2023) [Crossref]
• De Nardis et al., Correlation functions and transport coefficients in generalised hydrodynamics
  J. Stat. Mech. 2022, 014002 (2022) [Crossref]
• Durnin et al., Diffusive hydrodynamics of inhomogenous Hamiltonians
  J. Phys. A: Math. Theor. 54, 494001 (2021) [Crossref]
• Bulchandani et al., Superdiffusion in spin chains
  J. Stat. Mech. 2021, 084001 (2021) [Crossref]
• Bertini et al., Finite-temperature transport in one-dimensional quantum lattice models
  Rev. Mod. Phys. 93, 025003 (2021) [Crossref]
• Gopalakrishnan et al., Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems
  Annu. Rev. Condens. Matter Phys. 15, 159 (2024) [Crossref]
• Koch et al., Adiabatic formation of bound states in the one-dimensional Bose gas
  Phys. Rev. B 103, 165121 (2021) [Crossref]
• Lopez-Piqueres et al., Hydrodynamics of nonintegrable systems from a relaxation-time approximation
  Phys. Rev. B 103, L060302 (2021) [Crossref]
• Bouchoule et al., Generalized hydrodynamics in the one-dimensional Bose gas: theory and experiments
  J. Stat. Mech. 2022, 014003 (2022) [Crossref]
• Bastianello et al., Hydrodynamics of weak integrability breaking
  J. Stat. Mech. 2021, 114003 (2021) [Crossref]
• Scopa et al., Scaling of fronts and entanglement spreading during a domain wall melting
  Eur. Phys. J. Spec. Top. 232, 1763 (2023) [Crossref]