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We extend the recently developed causal superfermion approach to thereal-time transport theory to time-dependent decay problems.Its usefulness isillustrated for the Anderson model of a quantum dot with tunneling ratesdepending on spin due to the ferromagnetic electrodes and/or spin polarizationof the tunnel junction. We set up a second quantization scheme for densityoperators in the Liouville-Fock space constructing causal field superoperatorsusing the fundamental physical principles of causality/probability conservationand the fermion-parity superselection (univalence). The time-dependentperturbation series for the time-evolution is renormalized by explicitlyperforming the wide-band limit on the superoperator level. The short andlong-time reservoir correlations are shown to be tightly linked to theoccurrence 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 memorykernels in real-time. A remarkable feature of this approach is the naturalappearance of a measurable fermion-parity protected decay mode. It already canbe calculated exactly in the Markovian, infinite temperature limit by leadingorder perturbation theory, yet persists unaltered for the finite temperature,interaction and tunneling spin polarization. Furthermore, we show how aLiouville-space analog of the Pauli principle directly leads to the exactresult in the noninteracting limit: surprisingly, it is obtained in finite(second) order renormalized perturbation theory, both for the self-energy aswell as the time-evolution propagator. For this limit we calculate thetime-evolution of the full density operator starting from an arbitrary initialstate on the quantum dot, including spin and pairing coherences andtwo-particle correlations.

physical review. b, condensed matter and materials physics

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