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.

arXiv comment10 pages, 5 figures

References in corpus (19)

• Quantum Communication Through an Unmodulated Spin Chain
• Perfect state transfer in quantum spin networks
• 1/f noise: implications for solid-state quantum information
• Environment-independent decoherence rate in classically chaotic systems
• Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime
• Simulations of Information Transport in Spin Chains
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Quantum Dynamical Echoes in the Spin 'Diffusion' in Mesoscopic Systems
• Robustness of spin-coupling distributions for perfect quantum state transfer
• 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 Interference Phenomena in the Local Polarization Dynamics of Mesoscopic Systems: An NMR Observation
• Quantum parallelism as a tool for ensemble spin dynamics calculations
• Correlation effects in bistability at the nanoscale: steady state and beyond
• Quantum dynamical phase transition in a system with many-body interactions
• Nuclear Spin Dynamics in Double Quantum Dots: Multi-Stability, Dynamical Polarization, Criticality and Entanglement
• 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 (10)

• Decoherence in current induced forces: Application to adiabatic quantum motors
• Emergent decoherence induced by quantum chaos in a many-body system: A Loschmidt echo observation through NMR
• Dynamics and decoherence in nonideal Thouless quantum motors
• Loschmidt echo in many-spin systems: contrasting time-scales of local and global measurements
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Unified Theoretical Approach to Electronic Transport from Diffusive to Ballistic Regimes
• Role of energy uncertainties in ergodicity breaking induced by competing interactions and disorder. A dynamical assessment through the Loschmidt echo
• Simulating a Catalyst induced Quantum Dynamical Phase Transition of a Heyrovsky reaction with different models for the environment
• Universal stability of coherently diffusive 1D systems with respect to decoherence
• Mechanical rotation via optical pumping of paramagnetic impurities