Tunneling Dynamics and Time Delay in Electron Transport through Time-Dependent Barriers with Finite-Bandwidth Reservoirs

• URL: http://arxiv.org/abs/2507.20649v1
• Date: Mon, 28 Jul 2025 09:13:04 GMT
• Title: Tunneling Dynamics and Time Delay in Electron Transport through Time-Dependent Barriers with Finite-Bandwidth Reservoirs
• Authors: Shmuel Gurvitz, Dmitri Sokolovski,
• Abstract summary: We study a model system composed of a time-dependent tunneling barrier and two reservoirs of finite bandwidth.<n>We derive simple expressions for the time-dependent tunneling current in both adiabatic and non-adiabatic regimes.<n>Our findings provide a robust foundation for understanding tunneling dynamics in non-Markovian environments.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a transparent and analytically tractable approach to the problem of time-dependent electron transport through tunneling barriers. Using the Single-Electron Approach, we study a model system composed of a time-dependent tunneling barrier coupled to two reservoirs of finite bandwidth. Avoiding Floquet expansions, we derive simple expressions for the time-dependent tunneling current in both adiabatic and non-adiabatic regimes. Our formulation, based on the tunneling Hamiltonian framework, relates barrier modulation to measurable phase shifts in the steady-state current, offering a physically intuitive definition of the tunneling (or traversal) time. Remarkably, in the Markovian limit (wide-band reservoirs), we recover the well-known result of vanishing tunneling time. In contrast, for finite-bandwidth leads, we predict a finite time delay given by the inverse bandwidth. Our findings provide a robust foundation for understanding tunneling dynamics in non-Markovian environments and may serve as a benchmark for experimental investigations involving tunable band structures.

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