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Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states

We extend the recently developed causal superfermion approach to the real-time transport theory to time-dependent decay problems.Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to the ferromagnetic electrodes and/or spin polarization of the tunnel junction. We set up a second quantization scheme for density operators in the Liouville-Fock space constructing causal field superoperators using the fundamental physical principles of causality/probability conservation and the fermion-parity superselection (univalence). The time-dependent perturbation series for the time-evolution is renormalized by explicitly performing the wide-band limit on the superoperator level. The short and long-time reservoir correlations are shown to be tightly linked to the occurrence of causal field destruction and creation superoperators, respectively. The effective theory takes as a reference a damped local system, providing an interesting starting point for numerical calculations of memory kernels in real-time. A remarkable feature of this approach is the natural appearance of a measurable fermion-parity protected decay mode. It already can be calculated exactly in the Markovian, infinite temperature limit by leading order perturbation theory, yet persists unaltered for the finite temperature, interaction and tunneling spin polarization. Furthermore, we show how a Liouville-space analog of the Pauli principle directly leads to the exact result in the noninteracting limit: surprisingly, it is obtained in finite (second) order renormalized perturbation theory, both for the self-energy as well as the time-evolution propagator. For this limit we calculate the time-evolution of the full density operator starting from an arbitrary initial state on the quantum dot, including spin and pairing coherences and two-particle correlations.