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

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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.

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Authors and Affiliations

  1. Mathematisches Institute der Universität Leipzig, Augustusplatz 10/11, 04109, Leipzig, Germany

    Stephan Luckhaus

  2. Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103, Leipzig, Germany

    Luca Mugnai

Authors
  1. Stephan Luckhaus
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  2. Luca Mugnai
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Correspondence to Stephan Luckhaus.

Additional information

Communicated by Dr. Lev Truskinovsky.

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Luckhaus, S., Mugnai, L. On a mesoscopic many-body Hamiltonian describing elastic shears and dislocations. Continuum Mech. Thermodyn. 22, 251–290 (2010). https://doi.org/10.1007/s00161-010-0142-0

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  • DOI: https://doi.org/10.1007/s00161-010-0142-0

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