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As a liquid is progressively supercooled an intriguing weakening of thewavenumber ($q$) dependence of the structural relaxation time $\tau(q)$ in thelarge q limit is observed both in experiments and simulation studies. Neitherthe continuous Brownian diffusive dynamics nor the discontinuous activatedevents can alone explain the anomalous wavenumber dependence. Here we use ourrecently developed theory that unifies the mode coupling theory (MCT) forcontinuous dynamics and the random first order transition theory (RFOT)treatment of activated discontinuous motion as a nucleation (instanton)process, to understand the wavenumber dependence of density relaxation. Thepredicted smooth change in mechanism of relaxation from diffusive to activated,in the crossover regime, is wavevector dependent and is eventually responsiblefor sub-quadratic, almost linear, $q$ dependence of the relaxation time.

Wavenumber dependence of the structural relaxation time in the crossover regime of supercooled liquid dynamics