Dephasing versus collapse: Lessons from the tight-binding model with noise

TL;DR

This paper investigates how different environmental models affect wave function localization in a noisy tight-binding system, revealing that phase coherence loss and wave packet narrowing are not always directly correlated, complicating the quantum-classical transition understanding.

Contribution

It compares various unravellings of the Lindblad equation in a tight-binding model, highlighting the unique behavior of quantum-state diffusion in wave packet localization.

Findings

Quantum-state diffusion leads to slower wave packet narrowing than phase coherence loss.

Not all unravellings produce localized wave packets despite phase decoherence.

No unique wave function description exists without feedback, impacting quantum-classical transition studies.

Abstract

Condensed matter physics at room temperature usually assumes that electrons in conductors can be described as spatially narrow wave packets - in contrast to what the Schr\"odinger equation would predict. How a finite-temperature environment can localize wave functions is still being debated. Here, we represent the environment by a fluctuating potential and investigate different unravellings of the Lindblad equation that describes the one-dimensional tight-binding model in the presence of such a potential. While all unravellings show a fast loss of phase coherence, only part of them lead to narrow wave packets, among them the quantum-state diffusion unravelling. Surprisingly, the decrease of the wave packet width for the quantum state diffusion model with increasing noise strength is slower than that of the phase coherence length. In addition to presenting analytical and numerical results, we also provide phenomenological explanations for them. We conclude that as long as no feedback between the wave function and the environment is taken into account, there will be no unique description of an open quantum system in terms of wave functions. We consider this to be an obstacle to understanding the quantum-classical transition.