Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
67/2009

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

Stephan Luckhaus and Luca Mugnai

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.

Received:
Nov 19, 2009
Published:
Nov 25, 2009
Keywords:
dislocations, theory of defects

Related publications

inJournal
2010 Repository Open Access
Stephan Luckhaus and Luca Mugnai

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

In: Continuum mechanics and thermodynamics, 22 (2010) 4, pp. 251-290