ARPES of Bi₂Sr₂CaCu₂O_8+δinterpreted via a particle in a system of dynamic scatterers

Parabolic cylinder functions of the formAe-C2z2Dν(2Cz),withz=εG-ε, are employed to quantitatively describe angle-resolved photoemission spectroscopy (ARPES) spectra of overdoped Bi₂Sr₂CaCu₂O_8+δ(Bi2212) over the temperature range 6-140 K at the antinodalk-point. These functions arise as solutions for a particle moving in a system of random scatterers. The fitting parameters-the amplitudeA, spectral coherence scaleC, and energy shiftϵ^G-are determined directly from experimental data. At 140 K, the ARPES line shape is dominated by the solution corresponding to a one-dimensional random system (ν=-12). Systematic deviations are well captured by additional contributions withν=12and 32. As temperature is reduced, the amplitudes of these components increase, producing a depletion of spectral weight near the Fermi level and the emergence of a peak-dip structure associated with the pseudogap. Below the superconducting transition temperatureTc, an additional contribution withν=1emerges, enhancing the coherence peak. The inverse spectral coherence scale 1/C, which closely reflects the spectral linewidth, scales linearly with temperature aboveTc, suggesting a connection to Planckian dissipation in the strange-metal regime. Within this framework, the antinodal electronic states of overdoped Bi2212 can be viewed as a realization of a particle moving in a one-dimensional dynamic random environment, with systematic low-temperature corrections.