Abstract

We provide a theoretical framework to describe the quantum many-body
dynamics of Andreev states in Josephson junctions with spin-orbit
coupling and a magnetic Zeeman field. In such cases, employing a doubled
Nambu spinor description is technically advantageous but one then has to
be careful to avoid double-counting problems. By deriving the Lindblad
the master equation in the so-called excitation picture, we show that a
physically consistent many-body theory free from double-counting problems
follows. We apply our formalism to a study of dynamical parity
stabilization of the Andreev sector at intermediate times after an
initial microwave pulse, in particular addressing the combined effects
of spin-orbit coupling and Zeeman field.