Fermionic duality: General symmetry of open systems with strong dissipation and memory

Abstract

We consider the exact time-evolution of a broad class of fermionic open quantum systems with both strong interactions and strong coupling to wide-band reservoirs. We present a nontrivial fermionic duality relation between the evolution of states (Schrödinger) and of observables (Heisenberg). We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics, covering Kraus measurement operators, the Choi-Jamio lkowski state, time-convolution and convolutionless quantum master equations and generalized Lindblad jump operators. We discuss the insights this offers into the divisibility and causal structure of the dynamics and the application to nonperturbative Markov approximations and their initial-slip corrections. Our results underscore that predictions for fermionic models are already fixed by fundamental principles to a much greater extent than previously thought.

The connection between time-local and time-nonlocal perturbation expansions

“…This more powerful expansion was initially developed for K as first stage of a continuous RG-flow method for open quantum systems [5,47,48] to deal with strong dissipative coupling and non-equilibrium. It was later studied on its own merits [46,[49][50][51] and revealed powerful exact relations [50,52]. However, applications to the transient time-evolution of interacting systems analyzed in the present work were not yet explored.…”