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Self-organization, and transitions from reversible to irreversible behaviour,of interacting particle assemblies driven by externally imposed stresses ordeformation is of interest in comprehending diverse phenomena in soft matter.They have been investigated in a wide range of systems, such as colloidalsuspensions, glasses, and granular matter. In different density and drivingregimes, such behaviour is related to yielding of amorphous solids, jamming,and memory formation, \emph{etc.} How these phenomena are related to each otherhas not, however, been much studied. In order to obtain a unified view of thedifferent regimes of behaviour, and transitions between them, we investigatecomputationally the response of soft sphere assemblies to athermal cyclic sheardeformation over a wide range of densities and amplitudes of shear deformation.Cyclic shear deformation induces transitions from reversible to irreversiblebehaviour in both unjammed and jammed soft sphere packings. Well aboveisotropic jamming density ($\bf{\phi_J}$), this transition corresponds toyielding. In the vicinity of the jamming point, up to a higher density limit wedesignate ${\bf \phi_J^{cyc}}$, an unjammed phase emerges between a localised,\emph{absorbing} phase, and a diffusive, {\emph irreversible} phase. Theemergence of the unjammed phase signals the shifting of the jamming point tohigher densities as a result of annealing, and opens a window where shearjamming becomes possible for frictionless packings. Below $\bf{\phi_J}$, twodistinct localised states, termed point and loop reversibile, are observed. Wecharacterise in detail the different regimes and transitions between them, andobtain a unified density-shear amplitude phase diagram.

Unified phase diagram of reversible-irreversible, jamming and yielding transitions in cyclically sheared soft sphere packings