Emergent thermalization thresholds in unitary dynamics of inhomogeneously disordered quantum systems

Inspired by the avalanche scenario for many-body localization instability, we reverse the conventional setup and ask whether a large weakly disordered chain can thermalize a smaller, strongly disordered chain when the composite system evolves unitarily. Using transport as a dynamical probe, we identify three distinct thermalization regimes as a function of the disorder strength of the smaller chain: (i) complete thermalization with self-averaging at weak disorder, (ii) realization-dependent thermalization with strong sample-to-sample fluctuations at intermediate disorder, and (iii) absence of thermalization at strong disorder. We find that for a fixed length of the smaller chain, the non-self-averaging regime broadens with the size of the weakly disordered chain, revealing a nuanced interplay between disorder and system size. These results highlight how inhomogeneous disorder can induce emergent thermalization thresholds in closed quantum systems, providing direct access to disorder regimes where thermalization or its absence can be reliably observed.