THE FINITENESS OF THE NUMBER OF EIGENVALUES OF THE FOUR-PARTICLE SCHRÖDINGER OPERATOR WITH THREE-PARTICLE CONTACT INTERACTION

In this paper, we consider the four-particle Schr\"{o}dinger operator corresponding to the Hamiltonian of a system of four arbitrary quantum particles via a three-particle contact interaction potential on a three-dimensional lattice. The finiteness of the number of eigenvalues of the Schr\"{o}dinger operator lying to the left of the essential spectrum for zero value of the total quasi-momentum is proved.

Inversion of force lines in fiber-reinforced jammed granular material

Freestanding columns, built out of nothing but loose gravel and continuous strings can be stable even at several meters in height and withstand vertical loads high enough to severely fragment grains of the column core. We explain this counter-intuitive behavior through dynamic simulations with polyhedral rigid particles and elastic wire chains. We evaluate the fine structure of the particle contact networks, as well as confining forces and reveal fundamental intrinsic differences to the well-studied case of confining silos. Graphic abstract