| dc.description.abstract | The study of quantum many body physics occupies a special place in the landscape of theoretical science, as it behaves like a connective tissue between seemingly disparate domains of inquiry, such as computer science, condensed matter physics and quantum gravity. A major challenge in the field concerns the solvability of strongly-interacting, non-integrable models driven away from equilibrium. Usually, such models can be exactly solved numerically for small-N, or in certain cases one can access their early time behaviour analytically in the infinite-N limit.
In this work, we shed light on the Brownian SYK models as exactly-solvable candidates to study non-equilibrium quantum dynamics. We show that these models have emergent symmetry structures post disorder averaging, where the model built with Majorana fermions (without charge conservation) maps to SO(n) spins and the complex fermionic model with charge conservation maps to SU(n) spins, both of which evolve in imaginary time. This enables us to probe various kinds of dynamical properties, such as charge transport and information scrambling, at both large finite-N and in the infinite-N limit. Apart from the obvious advantage of exact numerical solvability at large-N, the hydrodynamic descriptions that emerge from these models are valid at all time scales, in contrast to other commonly used methods. In case of the model with U(1) symmetry, the emergent hydrodynamics also describe the coupling of the charge-transport with the operator dynamics for arbitrary charge density-profiles.
Using the insights gained from the U(1) symmetric model, we also explicitly demonstrate the difference between commonly used probes of dynamics, such as the Green’s functions, and more complicated higher-order correlators such the OTOC (out-of-time ordered correlator) in the study of non-equilibrium quantum dynamics. | |
