From Electronic Heterogeneity to Extreme Residence Times: A Multiscale Model of Energetic Stabilization, Stochastic Trapping, and Transport

Abstract

Persistent local states can arise without a uniform reduction in system-wide mobility.Here, we develop a minimal multiscale model to examine whether mi-croscopic electronic heterogeneity can propagate through energetic stabi-lization into extreme local residence-time statistics.A four-state effective Hamiltonian was used to generate distributionsof coupling-induced stabilization.The uncoupled reference energy was defined consistently with the four-state basis as the minimum energy of the uncoupled states.Electronic heterogeneity systematically broadened the resulting stabi-lization distribution.Across the investigated range, the standard deviation of the stabiliza-tion distribution increased by approximately 1.73-fold.The 99.9th percentile of stabilization increased by approximately 1.67-fold.These energetic distributions were then coupled to a stochastic trap-ping model through an energy-dependent escape probability.Increasing electronic heterogeneity produced a systematic increase inthe upper tail of the residence-time distribution.The ensemble-mean 99.9th percentile of residence time increased byapproximately 1.21-fold.In contrast, the effective diffusion coefficient remained nearly unchanged,with a high-to-low heterogeneity ratio of approximately 0.993.Thus, enhanced extreme local residence did not imply a comparablepopulation-level transport slowdown.To separate effects of mean stabilization from effects of distributionalheterogeneity, the coupled model was compared with a homogeneous mean-matched control.At the highest electronic heterogeneity, the coupled system showed amean increase in the 99.9th-percentile residence time of 2.55 simulationsteps relative to the mean-matched control.A paired bootstrap analysis gave a 95% confidence interval of [1.60, 3.55]for this mean difference.The corresponding mean residence-time ratio was approximately 1.105,with a 95% bootstrap confidence interval of [1.065, 1.145].This residual effect indicates that stabilization heterogeneity can influ-ence extreme residence statistics beyond the effect of mean stabilizationalone.A separate Liouvillian spectral-gap analysis found no evidence for di-rect coupling-induced relaxation slowdown within 10,201 scanned param-eter combinations.These results support a restricted multiscale mechanism in which mi-croscopic electronic heterogeneity broadens an effective stabilization land-scape, which is then transmitted through local escape dynamics and pref-erentially amplified in the extreme tail of residence-time statistics.The framework does not establish a direct mechanism for any specificclimatic, environmental, or biological phenomenon.Rather, it provides a testable theoretical basis for investigating howmicroscopic heterogeneity may contribute to rare, long-lived local statesin more complex nonequilibrium systems.