Achieving transitionless quantum driving in a many-particle system via coupling to an auxiliary many-particle system of opposing statistics

Transitionless quantum driving (TQD) in a quantum system driven by a time dependent Hamiltonian, $H_0(t)$, is in principle always possible via the addition of a counterdiabatic term, $H_1(t)$, as shown by Berry, and where $H_1(t)$ is in general nonlocal. Time dependence of $H_0$ gives rise to a curvature term in the comoving frame, which can be described via a gauge field, that induces transitions between different states, and whose influence is exactly nullified by $H_1(t)$. We explore an alternative way of achieving TQD in a many-particle quantum system (composed of either bosons or fermions), where all fields are coupled locally. In lieu of $H_1(t)$, we locally couple the original system A to a second system B (whose particles carry statistics opposite to A's) via a gaugino field. We explore the relationships between the A and B systems and the gauge and gaugino fields necessary to achieve TQD, and show that these relationships have a SUSY-like character. To illustrate, we explore the suppression of the Schwinger effect in a 1+1 D gas of Dirac electrons coupled to a time-dependent electric field that results from the suitable coupling (via gauginos) to its SUSY like partner.