Effective Forces in Thermal Amorphous Solids with Generic Interactions
arXiv:1808.00026 · doi:10.1103/PhysRevE.99.011001
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 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.
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References in corpus (15)
- Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture II: Intermediate Scattering Function and Dynamic Susceptibility
- Plastic Response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain-rate
- Universal Breakdown of Elasticity at the Onset of Material Failure
- Do Athermal Amorphous Solids Exist?
- Locality and Non-locality in Elasto-plastic Responses of Amorphous Solids
- On the rigidity of a hard sphere glass near random close packing
- Statistical Physics of Elasto-Plastic Steady States in Amorphous Solids: Finite Temperatures and Strain Rates
- Replica theory of the rigidity of structural glasses
- Predicting plastic flow events in athermal shear-strained amorphous solids
- Elasticity in Amorphous Solids: Nonlinear or Piece-Wise Linear?
- Linking high and low temperature plasticity in bulk metallic glasses: thermal activation, extreme value statistics and kinetic freezing
- How Generic are the Robust Theoretical Aspects of Jamming in Hard Sphere Models?
- Atomistic Simulations of Magnetic Amorphous Solids: Magnetostriction, Barkhausen noise and novel singularities
- Emergent Inter-particle Interactions in Thermal Amorphous Solids
- The Anatomy of Plastic Events in Magnetic Amorphous Solids