Description
In this study, we try to calculate the Thouless time by analyzing the spectral form factor, survival probability, and diffusion constant within the context of a spin-$1/2$ $XX$ ladder model. We employ numerical methods to compare the Thouless time extracted from these different observables. However, our preliminary results indicate inconsistencies between the methods, prompting concerns about the consistency and reliability of the extracted Thouless time. We examine potential sources of these inconsistencies, including finite-size effects, numerical precision, and the choice of parameters. This ongoing investigation aims to distinguish whether the possible discrepancies are intrinsic to the model or arise from methodological limitations, ultimately contributing to a more accurate characterization of the time scales in closed quantum systems.
