How low can you go?  Jamming in a system with just one degree of freedom per particle

We explore the free energy landscape and the set of locally optimal configurations for a system consisting of spheres with fixed positions and freely tunable radii.  We consider both hard sphere models (overlaps incur an infinite energy penalty) and soft-sphere models (overlaps incur a harmonic energy penalty).  In both cases, a critically jammed configuration can be defined as the set of radii for which there are no overlapping particles but increasing any radius will create an overlap.  For a given set of positions we present a method for enumerating all possible jammed configurations and thus revealing the structure of the landscape. We demonstrate bounds on the configurations which can be reached through purely local moves within the landscape, define the concept of an “inherent state”, and relate such configurations to the globally optimal configuration.  By including position as a quenched disorder, similarly to the random Lorentz gas (RLG), this model captures some aspects of the classical jamming scenario while promising a higher degree of mathematical tractability.