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For amorphous solids, it has been intensely debated whether the traditionalview on solids, in terms of the ground state and harmonic low energyexcitations on top of it, such as phonons, is still valid. Recent theoreticaldevelopments of amorphous solids revealed the possibility of unexpectedlycomplex free energy landscapes where the simple harmonic picture breaks down.Here we demonstrate that standard rheological techniques can be used aspowerful tools to examine non-trivial consequences of such complex free energylandscapes. By extensive numerical simulations on a hard sphere glass underquasi-static shear at finite temperatures, we show that, above the so-calledGardner transition density, the elasticity breaks down, the stress relaxationexhibits slow and aging dynamics, and the apparent shear modulus becomesprotocol-dependent. Being designed to be reproducible in laboratories, ourapproach may trigger explorations of the complex free energy landscapes of alarge variety of amorphous materials.

Exploring the complex free energy landscape of the simplest glass by rheology