Abstract
We study the non-equilibrium dynamics of a one-dimensional complex
Sachdev-Ye-Kitaev chain by directly solving for the steady state Green's
functions in terms of small perturbations around their equilibrium values. The
model exhibits strange metal behavior without quasiparticles and features
diffusive propagation of both energy and charge. We explore the thermoelectric
transport properties of this system by imposing uniform temperature and
chemical potential gradients. We then expand the conserved charges and their
associated currents to leading order in these gradients, which we can compute
numerically and analytically for different parameter regimes. This allows us to
extract the full temperature and chemical potential dependence of the transport
coefficients. In particular, we uncover that the diffusivity matrix takes on a
simple form in various limits and leads to simplified Einstein relations. At
low temperatures, we also recover a previously known result for the
Wiedemann-Franz ratio. Furthermore, we establish a relationship between
diffusion and quantum chaos by showing that the diffusivity eigenvalues are
upper bounded by the chaos propagation rate at all temperatures. Our work
showcases an important example of an analytically tractable calculation of
transport properties in a strongly interacting quantum system and reveals a
more general purpose method for addressing strongly coupled transport.