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In marginally jammed solids confined by walls, we calculate the particle andensemble averaged value of an order parameter, $\left<\Psi(r)\right>$, as afunction of the distance to the wall, $r$. Being a microscopic indicator ofstructural disorder and particle mobility in solids, $\Psi$ is by definitionthe response of the mean square particle displacement to the increase oftemperature in the harmonic approximation and can be directly calculated fromthe normal modes of vibration of the zero-temperature solids. We find that, inconfined jammed solids, $\left<\Psi(r)\right>$ curves at different pressurescan collapse onto the same master curve following a scaling function,indicating the criticality of the jamming transition. The scaling collapsesuggests a diverging length scale and marginal instability at the jammingtransition, which should be accessible to sophisticatedly designed experiments.Moreover, $\left<\Psi(r)\right>$ is found to be significantly suppressed whenapproaching the wall and anisotropic in directions perpendicular and parallelto the wall. This finding can be applied to understand the $r$-dependence andanisotropy of the structural relaxation in confined supercooled liquids,providing another example of understanding or predicting behaviors ofsupercooled liquids from the perspective of the zero-temperature amorphoussolids.

Jamming in confined geometry: Criticality of the jamming transition and implications of structural relaxation in confined supercooled liquids