# American Institute of Mathematical Sciences

January  2010, 9(1): 61-75. doi: 10.3934/cpaa.2010.9.61

## Infinite harmonic chain with heavy mass

 1 University of Oxford, Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB 2 Dipartimento di Matematica "F. Casorati", Universitá di Pavia, via Ferrata 1, P.O. Box 27100, Pavia

Received  January 2009 Revised  June 2009 Published  October 2009

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.
Citation: Michael Herrmann, Antonio Segatti. Infinite harmonic chain with heavy mass. Communications on Pure & Applied Analysis, 2010, 9 (1) : 61-75. doi: 10.3934/cpaa.2010.9.61
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