Dynamic disorder, trap renormalization, and diffusion on rugged energy landscapes

Diffusion in rugged energy landscapes is central to chemical physics, with relevance to glasses, disordered solids, and biomolecular motion. Most theories assume quenched disorder, but in many condensed-phase and biological systems, local energies fluctuate because of solvent reorganization, structural relaxation, or conformational change. A region that is strongly trapping at one time may become less confining later. We develop a minimal theory for one-dimensional diffusion on a rugged site-energy landscape containing quenched Gaussian disorder and dichotomic fluctuations. The key objects are rare three-site traps (TSTs): a low-energy central site flanked by two higher-energy neighbors. Such TSTs suppress diffusion because the walker cannot bypass them and may revisit the same local environment repeatedly. The fluctuating triplet has eight environmental configurations, from which we obtain the mean residence time and the probabilities of escape to the left and right. Repeated departures and returns are incorporated through a memory factor that compares the return-time distribution of the walker with the relaxation of the local environment. Temporal fluctuations weaken transport bottlenecks by reducing the persistence of TSTs. In the quasi-quenched regime, the walker repeatedly encounters nearly the same trap, and the static Banerjee, Biswas, Seki, and Bagchi correction remains operative. In the rapidly renewed regime, the environment changes before return, shortening trap lifetimes and restoring Zwanzig-like transport. The crossover is governed jointly by hopping, environmental renewal, and return dynamics.