Effective Forces in Thermal Amorphous Solids with Generic Interactions
Abstract
In thermal glasses at temperatures sufficiently lower than the glass transition, the constituent particles are trapped in their cages for sufficiently long time such that their {\em timeaveraged positions} can be determined before diffusion and structural relaxation takes place. The effective forces are those that hold these average positions in place. In numerical simulations the effective forces $\B F_{ij}$ between any pair of particles can be measured as a time average of the {\em bare} forces $\B f_{ij}(\B r_{ij}(t))$. In general even if the bare forces come from twobody interactions, thermal dynamics dress the effective forces to contain manybody interactions. Here we develop the effective theory for systems with generic interactions, where the effective forces are derivable from an effective potential and in turn they give rise to an effective Hessian whose eigenvalues are all positive when the system is stable. In this Letter we offer analytic expressions for the effective theory, and demonstrate the usefulness and the predictive power of the approach.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 arXiv:
 arXiv:1808.00026
 Bibcode:
 2018arXiv180800026P
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 2 figures