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

Abstract

We present a model for decoherence in time-dependent transport. 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. We show 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 whith a local energy fluctuation. A two-spin system is reduced to a two level system (TLS) that oscillates among $|0⟩$ $\equiv$ $|\uparrow \downarrow ⟩$ and $|1⟩\equiv$ $|\downarrow \uparrow ⟩$. We show that QD model recovers not only the exponential damping of the oscillations in the low perturbation regime, but also the non-trivial 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. The QD average 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. Because 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.

10 pages, 5 figures

References in corpus (8)

• Simulations of Information Transport in Spin Chains
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Transport in a disordered tight-binding chain with dephasing
• Revisiting the Fermi Golden Rule: Quantum Dynamical Phase Transition as a Paradigm Shift
• Disorder and dephasing effect on electron transport through conjugated molecular wires in molecular junctions
• Quantum parallelism as a tool for ensemble spin dynamics calculations
• Decoherence under many-body system-environment interactions: a stroboscopic representation based on a fictitiously homogenized interaction rate
• On the low frequency electromagnetic waves in quasi-two-dimensional metals

Cited by in corpus (1)

• Mechanical rotation via optical pumping of paramagnetic impurities