An upper bound on transport
arXiv:1706.00019 · doi:10.1103/PhysRevLett.119.141601
Abstract
The linear growth of operators in local quantum systems leads to an effective lightcone even if the system is non-relativistic. We show that consistency of diffusive transport with this lightcone places an upper bound on the diffusivity: . The operator growth velocity defines the lightcone and is the local equilibration timescale, beyond which the dynamics of conserved densities is diffusive. We verify that the bound is obeyed in various weakly and strongly interacting theories. In holographic models this bound establishes a relation between the hydrodynamic and leading non-hydrodynamic quasinormal modes of planar black holes. Our bound relates transport data --- including the electrical resistivity and the shear viscosity --- to the local equilibration time, even in the absence of a quasiparticle description. In this way, the bound sheds light on the observed -linear resistivity of many unconventional metals, the shear viscosity of the quark-gluon plasma and the spin transport of unitary fermions.
6 pages. 1 figure. v2 streamlined and improved presentation
References in corpus (24)
- Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
- Causality, Analyticity and an IR Obstruction to UV Completion
- Phenomenology of fully many-body-localized systems
- Relativistic viscous hydrodynamics, conformal invariance, and holography
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Viscosity, Black Holes, and Quantum Field Theory
- Viscosity Bound and Causality Violation
- Theory of universal incoherent metallic transport
- Quantum Criticality
- Universal Quantum Viscosity in a Unitary Fermi Gas
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
- Momentum dissipation and effective theories of coherent and incoherent transport
- Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches
- Quantum chaos on a critical Fermi surface
- Time evolution of correlations in strongly interacting fermions after a quantum quench
- Thermodynamic Measurements in a Strongly Interacting Fermi Gas
- Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade
- Diffusion and Chaos from near AdS horizons
- Charge diffusion and the butterfly effect in striped holographic matter
- Quantum mechanical limitations to spin diffusion in the unitary Fermi gas
- Observation of the Leggett-Rice effect in a unitary Fermi gas
- Gravitational quasinormal modes of AdS black branes in d spacetime dimensions