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

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