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)
published in: Continuum mechanics and thermodynamics, 22 (2010) 4, p. 251-290
DOI number (of the published article): 10.1007/s00161-010-0142-0
Keywords and phrases: dislocations, theory of defects
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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.