Speaker
Raghu Mahajan
(IAS)
Description
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: D<=v^2 \tau_eq. The operator growth velocity v
defines the lightcone and \tau_eq 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 T-linear resistivity of many
unconventional metals, the shear viscosity of the
quark-gluon plasma and the spin transport of unitary fermions.
