Speaker
Description
I consider a class of spinless-fermion Lindblad equations that exhibit decoupled BBGKY hierarchies. Importantly these do not describe “free” evolution in the sense that there is no Wick’s theorem and multi-point correlation functions cannot be reduced to two-point functions. In the cases where particle number is conserved, their late time behaviour is characterized by diffusive dynamics, leading to an infinite temperature steady state. Some of these models are Yang-Baxter integrable, others are not. The simple structure of the BBGKY hierarchy makes it possible to map the dynamics of Heisenberg-picture operators on few-body imaginary-time Schrödinger equations with non-Hermitian Hamiltonians. I use this formulation to obtain exact hydrodynamic projections of operators quadratic in fermions, and to determine linear response functions in Lindbladian non-equilibrium dynamics.
