On a mesoscopic many-body Hamiltonian describing elastic shears and dislocations

Stephan Luckhaus and Luca Mugnai

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Submission date: 19. Nov. 2009 (revised version: April 2010)
Pages: 47
published in: Continuum mechanics and thermodynamics, 22 (2010) 4, p. 251-290 
DOI number (of the published article): 10.1007/s00161-010-0142-0
Bibtex
Keywords and phrases: dislocations, theory of defects
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Abstract:
We define a ``reference-free'' many-body Hamiltonian acting on finite systems of particles, and study some properties of ``low-energy'' states. More precisely we show that ``low-energy'' states are locally well described (on a mesoscale) by appropriate affine transformations of a ground state lattice. Moreover we use such (local) description to define an ``holonomy representation map'' and a consequent notion of topological defect.