Decoherent time-dependent transport beyond the Landauer-Büttiker formulation: A quantum-drift alternative to quantum jumps

Abstract

We develop and implement a model for decoherence in time-dependent transport. Inspired in a dynamical formulation of the Landauer-Büttiker equations, it boils down into a form of wave function that undergoes a smooth stochastic drift of the phase in a local basis, the quantum-drift (QD) model. This drift is nothing else but a local energy fluctuation. Unlike quantum-jumps (QJ) models, no jumps are present in the density as the evolution is unitary. As a first application, we address the transport through a resonant state |0〉 that undergoes decoherence. Its numerical resolution shows the equivalence with the decoherent steady-state transport in presence of a Büttiker's voltage probe. In order to test the dynamics we consider two many-spin systems, which are cases of experimental interest, where a local energy fluctuation is a natural phenomenon. A two-spin system is reduced to a two-level system (TLS) that oscillates among |0〉≡|↑↓〉 and |1〉≡|↓↑〉. We show that the QD model recovers not only the exponential damping of the oscillations in the low perturbation regime, but also the nontrivial bifurcation of the damping rates at a critical point, i.e., the quantum dynamical phase transition. We also address the spin-wave-like dynamics of local polarization in a spin chain. By averaging over Ns realizations, the QD solution has about half the dispersion respect to the mean dynamics than QJ. By evaluating the Loschmidt echo (LE), we find that the pure states |0〉≡|↑↓〉 and |1〉≡|↓↑〉 are quite robust against the local decoherence. In contrast, the LE, and hence coherence, decays faster when the system is in a superposition state (|↑↓〉±|↓↑〉)/2, which is consistent with the general trend recently observed in spin systems through NMR. Because of its simple implementation, the method is well suited to assess decoherent transport problems as well as to include decoherence in both one-body and many-body dynamics.