Asymptotics of resolvent integrals: The suppression of crossings for analytic lattice dispersion relations

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dc.creatorLukkarinen, Jani
dc.date2006-04-20
dc.date.accessioned2026-07-07T07:45:16Z
dc.date.available2026-07-07T07:45:16Z
dc.descriptionWe study the so called crossing estimate for analytic dispersion relations of periodic lattice systems in dimensions three and higher. Under a certain regularity assumption on the behavior of the dispersion relation near its critical values, we prove that an analytic dispersion relation suppresses crossings if and only if it is not a constant on any affine hyperplane. In particular, this will then be true for any dispersion relation which is a Morse function. We also provide two examples of simple lattice systems whose dispersion relations do not suppress crossings in the present sense.
dc.description47 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0604049
dc.identifierhttp://arxiv.org/abs/math-ph/0604049
dc.identifierJ. Math. Pures Appl. 87 (2007) 193-225
dc.identifierdoi:10.1016/j.matpur.2006.11.003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123477
dc.subjectMathematical Physics
dc.subject74J20; 26D15
dc.titleAsymptotics of resolvent integrals: The suppression of crossings for analytic lattice dispersion relations
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