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Nonergodicity observed in single-particle tracking experiments is usuallymodeled by transient trapping rather than spatial disorder. We introduce modelsof a particle diffusing in a medium consisting of regions with random sizes andrandom diffusivities. The particle is never trapped, but rather performscontinuous Brownian motion with the local diffusion constant. Under simpleassumptions on the distribution of the sizes and diffusivities, we find thatthe mean squared displacement displays subdiffusion due to non-ergodicity forboth annealed and quenched disorder. The model is formulated as a walkcontinuous in both time and space, similar to the L\'{e}vy walk.

Nonergodic Subdiffusion from Brownian Motion in an Inhomogeneous Medium