title: Emergent interparticle interactions in thermal amorphous solids.
abstract: Amorphous media at finite temperatures, be them liquids, colloids, or glasses, are made of interacting particles that move chaotically due to thermal energy, continuously colliding and scattering off each other. When the average configuration in these systems relaxes only at long times, one can introduce effective interactions that keep the mean positions in mechanical equilibrium. We introduce a framework to determine the effective force laws that define an effective Hessian that can be employed to discuss stability properties and the density of states of the amorphous system. We exemplify the approach with a thermal glass of hard spheres; these experience zero forces when not in contact and infinite forces when they touch. Close to jamming we recapture the effective interactions that at temperature T depend on the gap h between spheres as T/h [C. Brito and M. Wyart, Europhys. Lett. 76, 149 (2006)EULEEJ0295-507510.1209/epl/i2006-10238-x]. For hard spheres at lower densities or for systems whose binary bare interactions are longer ranged (at any density), the emergent force laws include ternary, quaternary, and generally higher-order many-body terms, leading to a temperature-dependent effective Hessian.
authors.affiliation: Faculty of Mechanical Engineering, Technion, Haifa 3200003, Israel.
authors.forename: Oleg
authors.initials: O
authors.lastname: Gendelman
authors.affiliation: Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
authors.forename: Edan
authors.initials: E
authors.lastname: Lerner
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Yoav G
authors.initials: YG
authors.lastname: Pollack
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Itamar
authors.initials: I
authors.lastname: Procaccia
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Corrado
authors.initials: C
authors.lastname: Rainone
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Birte
authors.initials: B
authors.lastname: Riechers