Diffusion and superdiffusion from hydrodynamic projections

Abstract

Hydrodynamic projections, the projection onto conserved charges representing ballistic propagation of fluid waves, give exact transport results in many-body systems, such as the exact Drude weights. Focussing one one-dimensional systems, I show that this principle can be extended beyond the Euler scale, in particular to the diffusive and superdiffusive scales. By hydrodynamic reduction, Hilbert spaces of observables are constructed that generalise the standard space of conserved densities and describe the finer scales of hydrodynamics. The Green-Kubo formula for the Onsager matrix has a natural expression within the diffusive space. This space is associated with quadratically extensive charges, and projections onto any such charge give generic lower bounds for diffusion. In particular, bilinear expressions in linearly extensive charges lead to explicit diffusion lower bounds calculable from the thermodynamics, and applicable for instance to generic momentum-conserving one-dimensional systems. Bilinear charges are interpreted as covariant derivatives on the manifold of maximal entropy states, and represent the contribution to diffusion from scattering of ballistic waves. An analysis of fractionally extensive charges, combined with clustering properties from the superdiffusion phenomenology, gives lower bounds for superdiffusion exponents. These bounds reproduce the predictions of nonlinear fluctuating hydrodynamics, including the Kardar-Parisi-Zhang exponent 2/3 for sound-like modes, the Levy-distribution exponent 3/5 for heat-like modes, and the full Fibonacci sequence.

v1: 47 pages. v2: 64 pages, structure improved, section added with more intuitive explanations; accepted for publication in J. Stat. Phys

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Cited by in corpus (17)

• Ballistic macroscopic fluctuation theory
• Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
• Generalized hydrodynamics: a perspective
• Anomalous transport from hot quasiparticles in interacting spin chains
• Hydrodynamics and the eigenstate thermalization hypothesis
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Non-Gaussian diffusive fluctuations in Dirac fluids
• Diffusive hydrodynamics from long-range correlations
• A Bound on Thermalization from Diffusive Fluctuations
• Long-time dynamics in quantum spin lattices: ergodicity and hydrodynamic projections at all frequencies and wavelengths
• Subdiffusive transport in the Fredkin dynamical universality class
• Ruelle-Pollicott resonances of diffusive U(1)-invariant qubit circuits
• Diffusive hydrodynamics of hard rods from microscopics
• Simulating generalised fluids via interacting wave packets evolution
• Subexponential decay of local correlations from diffusion-limited dephasing
• Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies
• Quantum transport in 1D Hubbard model: Drude weights and Seebeck effect