Probabilistic configurations for thick braneworld in modified symmetric teleparallel gravity

In this research, we delve into the localization patterns of fermionic fieldswithin a braneworld setting, employing a modified gravity model denoted as$f(Q)$. Our investigation revolves around two specific models, $f_1(Q)=Q+kQ^n$and $f_2(Q)=Q+k_1Q^2+k_2Q^3$, where we systematically vary the parameters $n$and $k_{1,2}$. Through an in-depth analysis encompassing the effectivepotential, massless, and massive modes, we elucidate how deviations from theconventional symmetric teleparallel equivalent of general relativity (STEGR)gravity impact the localization of fermionic fields. To ensure greaterprecision, our methodology integrates probabilistic measures such as Shannonentropy and relative probability. Moreover, we gauge the stability of thesemodels employing differential configurational entropy (DCE), revealing acompelling correlation between the most stable configurations and the emergenceof novel structures within the background scalar field. This work significantlycontributes to our understanding of the gravitational modifications' intricateinfluence on fermionic field localization within braneworld scenarios. Byshedding light on these dynamics, it advances the broader comprehension of theinterplay between gravity modifications and fermionic field behaviors in thesetheoretical frameworks.