Infinite harmonic chain with heavy mass
- Herrmann, Michael
- Segatti, Antonio
2010 Mathematics Subject Classification
- 37K60 70F45
- Harmonic lattice, atomic chain, macroscopic continuum limit
Modelling a crystal with impurities we study an atomic chain of point masses with linear nearest neighbour interactions. We assume that the masses of the particles are normalised to $1$, except for one heavy particle which has mass $M$. We investigate the macroscopic behaviour of such a system when $M$ is large, and time and space are scaled accordingly. As main result we derive a PDE for the light particles that is coupled with an ODE for the heavy particle.