Stability of classical planar dipole matter on regular and aperiodic lattices

Abstract

The stability of matter is a historical problem that tackles the linearity of the bulk energy with the total number of particles M. The classical and quantum variants have been proved using mostly Coulomb interaction between electrons and nuclei, either fixed or submitted to thermal fluctuation. The classical dipole−dipole interaction is addressed here as the sole energy on regular tilings. We prove that the system on any regular (periodic) grid is always stable. The aperiodic or quasicrystal instance is conjectured and numerically illustrated for the particular cases of the Penrose P2 and the recently discovered hat monotiles.

Graphical abstract

Keywords

dipole−dipole interaction / periodic lattices / aperiodic lattices / stability of matter

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Higher Education Press