Packing spheres efficiently in large dimension d is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize a lower bound on the packing density. Our results suggest that exponentially many (in the number of particles) distinct disordered sphere packings can be efficiently constructed by this method, up to a packing fraction close to 7 d 2(-d). The latter is determined by solving the inverse problem of maximizing the dynamical glass transition over the space of the interaction potentials. Our method crucially exploits a recent exact formulation of the thermodynamics and the dynamics of simple liquids in infinite dimension.
Generating dense packings of hard spheres by soft interaction design / Maimbourg, T; Sellitto, M; Semerjian, G; Zamponi, F. - In: SCIPOST PHYSICS. - ISSN 2542-4653. - 4:6(2018). [10.21468/SciPostPhys.4.6.039]
Generating dense packings of hard spheres by soft interaction design
Zamponi F
2018
Abstract
Packing spheres efficiently in large dimension d is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize a lower bound on the packing density. Our results suggest that exponentially many (in the number of particles) distinct disordered sphere packings can be efficiently constructed by this method, up to a packing fraction close to 7 d 2(-d). The latter is determined by solving the inverse problem of maximizing the dynamical glass transition over the space of the interaction potentials. Our method crucially exploits a recent exact formulation of the thermodynamics and the dynamics of simple liquids in infinite dimension.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.