ARPES of Bi ₂ Sr ₂ CaCu ₂ O _8+delta interpreted via a particle in a system of dynamic scatterers

Parabolic cylinder functions of the form Ae^{(-<i>C</i>2_z2)}D_v(2<i>Cz</i>), with z=epsilon^G-epsilon, are employed to quantitatively describe angle-resolved photoemission spectroscopy (ARPES) spectra of overdoped Bi₂Sr₂CaCu₂O_8+delta(Bi2212) over the temperature range 6 - 140 K at the antinodal k-point. These functions arise as solutions for a particle moving in a system of random scatterers. The fitting parameters-the amplitude<i>A</i>, spectral coherence scale<i>C</i>, and energy shift<i>epsilonG</i>- 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 (<i>v</i>= -1/2). Systematic deviations are well captured by additional contributions with<i>v</i>=1/2 and 3/2. 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 temperature<i>T</i>_c, an additional contribution with<i>v</i>=1 emerges, enhancing the coherence peak. The inverse spectral coherence scale 1/<i>C</i>, which closely reflects the spectral linewidth, scales linearly with temperature above<i>T</i>_csuggesting 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.&#xD.