Non-hermitian Dirac theory from Lindbladian dynamics

This study investigates the intricate relationship between dissipative processes of open quantum systems and the non-Hermitian quantum field theory of relativistic fermionic systems. By examining the influence of dissipative effects on Dirac fermions via Lindblad formalism, we elucidate the effects of coupling relativistic Dirac particles with the environment and show the lack of manifest Lorentz invariance. Employing rigorous theoretical analysis, we generalize the collisionless Boltzmann equations for the relativistic dissipation-driven fermionic system and find the Lyapunov equation, which governs the stationary solutions. Using our formalism, one presents a simple non-Hermitian model that the relativistic fermionic particles and anti-particles are stable. Going further, using the solution to the Lyapunov equations, one analyses the effect of dissipation on the stationary charge imbalance of this non-Hermitian model and finds that the dissipation can induce a new kind of charge imbalance compared with the collisionless equilibrium case.