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The mechanism of diffusion in supercooled liquids is investigated from the potential energy landscape point of view, with emphasis on the crossover from high- to low-T dynamics. Molecular dynamics simulations with a time dependent mapping to the associated local mininum or inherent structure (IS) are performed on unit-density Lennard-Jones (LJ). New dynamical quantities introduced include r2_{is}(t), the mean-square displacement (MSD) within a basin of attraction of an IS, R2(t), the MSD of the IS itself, and g_{loc}(t) the mean waiting time in a cooperative region. At intermediate T, r2_{is}(t) posesses an interval of linear t-dependence allowing calculation of an intrabasin diffusion constant D_{is}. Near T_{c} diffusion is intrabasin dominated with D = D_{is}. Below T_{c} the local waiting time tau_{loc} exceeds the time, tau_{pl}, needed for the system to explore the basin, indicating the action of barriers. The distinction between motion among the IS below T_{c} and saddle, or border dynamics above T_{c} is discussed.
We numerically study the relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of temperatures. In a mean-field Mari-Kurchan model, we find tha
Thermal energy can be conducted by different mechanisms including by single particles or collective excitations. Thermal conductivity is system-specific and shows a richness of behaviors currently explored in different systems including insulators, s
The inherent structures ({it IS}) are the local minima of the potential energy surface or landscape, $U({bf r})$, of an {it N} atom system. Stillinger has given an exact {it IS} formulation of thermodynamics. Here the implications for the equation of
The self-diffusion constant D is expressed in terms of transitions among the local minima of the potential (inherent structure, IS) and their correlations. The formulae are evaluated and tested against simulation in the supercooled, unit-density Lenn
Configurational states that are to be associated, according to Goldstein, with the basins in the potential energy landscape cannot be characterized by any particular basin identifier such as the basin minima, the lowest barrier, the most probable ene