Emergent interparticle interactions in thermal amorphous solids

Abstract

Emergent interparticle interactions in thermal amorphous solidsGendelman, O.; Lerner, E.; Pollack, Y.G.; Procaccia, I.; Rainone, C.; Riechers, B. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. 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)]. 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.

Emergent power-law interactions in disordered crystals

“…Here F j (0) is 1. The displacement fields along the x and y directions produced by a single defect satisfy the following symmetry properties δx (1) (x, y) = −δx (1) (−x, y), δy (1) (x, y) = −δy (1) (x, −y).…”

“…Introduction: Emergent interactions arise in many microscopic theories of matter [1][2][3][4]. A paradigmatic example is the Lennard-Jones interaction that emerges as an induced dipole effect of polarizable constituents [5][6][7].…”

“…The incremental radii {δσ} and the lower order displacement fields act as sources that generate the displacement fields at higher orders. At linear order, the displacements in Fourier space as a response to the disorder {δσ i } can be expressed as δr µ, (1) ( k) = Gµ ( k)δσ( k) [39]. Here δσ( k) = k e i k• r δσ( r), δr µ refers to δx and δy for µ = x, y respectively, and Gµ ( k) represent the response Green's functions in Fourier space.…”

Higher-order corrections to the effective potential close to the jamming transition in the perceptron model

“…No analytical predictions about the typical scaling of the forces taking into account also subleading terms are available. Several numerical simulations have been carried out attempting to explain the observed behavior [35,38]. In particular, in [16,35] the authors showed that the deviation of the force from its leading behavior can be estimated numerically in molecular dynamics and the subleading term should be of order of the number of effective contacts δz = z − z c .…”

Effective forces in thermal amorphous solids with generic interactions

“…The effective forces in thermal systems are determined by the momentum transferred when particles interact. Even when the bare forces are binary, the effective forces contain ternary, quaternary and higher order terms [10,11]. In order to lift the methods that were so useful at T = 0 one needs a new idea: in thermal systems the particle positions are indeed not stationary, but in glasses with large relaxation times one can determine the time-averaged positions before the onset of diffusion and much before the glass relaxes to thermodynamic equilibrium [12].…”