Superdiffusive Transport in Open Quantum System

Most open quantum system models described by Lindblad master equation in previous literature exhibit diffusive transport. In this study, we explore the transport dynamics of the Lindblad master equation with free fermion Hamiltonian and quasi-particle projector Lindblad operator. We reveal that when the momentum distribution of quasi-particles has nodal points, superdiffusive transport could emerge. By studying the dynamics of the Wigner function, we rigorously elucidate how the dynamics of these enduring modes give rise to Levy walk processes, a renowned mechanism underlying superdiffusion phenomena. Our research not only demonstrates the controllability of dynamical scaling exponents through the selection of quasi-particles but also extends its applicability to higher dimensions, underlining the pervasive nature of superdiffusion in dephasing models.