Quantum theory of dissipative topological systems

We develop a quantum theory for topological systems incorporating dissipations, noises, and thermal effects with strong non-Markovian dynamics, while other approaches in the literature may not be applicable. We derive the exact master equation and transient quantum transport for the study of dissipative topological systems, mainly focusing on noninteracting topological insulators and topological superconductors. The resulting exact master equation is also applicable to systems initially entangled with environments. In this theory, dissipations and topological states can be related to each other through spectral densities which tie up the reservoir spectra and topological-state wave functions in the system-reservoir couplings when either the system or environment is a topological system. We also apply the theory to study quantized Majorana conductance in superconductor-semiconductor hybrid systems incorporating different dissipations, noises, and thermal effects.