Effective forces in thermal amorphous solids with generic interactions
| Autor: | Giorgio Parisi, Jacques Zylberg, Carmel A. B. Z. Shor, Itamar Procaccia |
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| Rok vydání: | 2018 |
| Předmět: |
Hessian matrix
Physics Condensed matter physics FOS: Physical sciences Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Condensed Matter - Soft Condensed Matter 01 natural sciences 010305 fluids & plasmas Amorphous solid symbols.namesake 0103 physical sciences Thermal symbols Effective field theory Relaxation (physics) Soft Condensed Matter (cond-mat.soft) Diffusion (business) 010306 general physics Glass transition Eigenvalues and eigenvectors |
| Zdroj: | Physical review. E. 99(1-1) |
| ISSN: | 2470-0053 |
| Popis: | 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 time-averaged 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 two-body interactions, thermal dynamics dress the effective forces to contain many-body 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. Comment: 2 figures |
| Databáze: | OpenAIRE |
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