From Localized Packets to Plane Waves: A Time-Domain Approach to Transport in Mesoscopic Systems

Quantum transport in mesoscopic systems is conventionally formulated within the Landauer--B\"uttiker scattering framework, where steady-state currents emerge from the transmission of plane waves representing propagating carriers. While highly successful, this description obscures the explicit time-domain dynamics of individual fermionic excitations and their role in establishing macroscopic transport. Here, we present an exact and self-contained time-domain construction of Landauer transport based on a discrete basis of orthogonal fermionic wave packets. Starting from a second-quantized formulation, we define packet creation operators via a continuous Fourier transform over a finite transport energy window. By encoding the Pauli exclusion principle, which enforces a fundamental temporal spacing $\Delta t = h/eV$, the current is reproduced in terms of orthogonal wave packets that are used for the rigorous construction of the many-body fermionic state. In this representation, a noiseless current emerges as a deterministic sequence of charge-carrying events, yielding the Landauer conductance $G_0 = e^2/h$ without invoking momentum-space kinematics. We further demonstrate that this construction remains exact for arbitrary energy dispersion. Additionally, the underlying Fock space decomposition into finite disjoint energy sub-bands renders the numerical approach highly scalable for high performance computing platforms. Our results establish a direct and rigorous bridge between the continuous scattering description of quantum transport and a discrete, time-resolved picture based on fermionic wave packets.