Decoherent time-dependent transport beyond the Landauer-B\"uttiker formulation: a quantum-drift alternative to quantum jumps

TL;DR

This paper introduces the Quantum Drift model as a wave function-based approach to simulate decoherence in time-dependent transport, offering advantages over quantum jump models and capturing complex dynamical phenomena.

Contribution

The Quantum Drift model provides a unitary, wave function-based alternative to quantum jumps for simulating decoherence, accurately capturing damping and phase transitions in quantum transport.

Findings

QD recovers exponential damping of oscillations

QF captures bifurcation of damping rates at critical points

Pure states are robust against local decoherence

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 $\left\vert 0\right\rangle $ that undergoes decoherence. We show the equivalence with the decoherent steady state transport in presence of a B\"{u}ttiker'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 $\left\vert 0\right\rangle $ $\equiv $ $ \left\vert \uparrow \downarrow \right\rangle $ and $\left\vert 1\right\rangle \equiv $ $\left\vert \downarrow \uparrow \right\rangle $. 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 $\left\vert 0\right\rangle $ and $\left\vert 1\right \rangle $ 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.