Numerical techniques for solving the quantum constraint equation of generic lattice-refined models in loop quantum cosmology

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dc.creatorNelson, William
dc.creatorSakellariadou, Mairi
dc.date2008-03-31
dc.date.accessioned2026-07-07T12:14:21Z
dc.date.available2026-07-07T12:14:21Z
dc.descriptionTo avoid instabilities in the continuum semi-classical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. The lattice refinement leads to new dynamical difference equations which, in general, do not have a uniform step-size, implying complications in their analysis and solutions. We propose a numerical method based on Taylor expansions, which can give us the necessary information to calculate the wave-function at any given lattice point. The method we propose can be applied in any lattice-refined model, while in addition the accuracy of the method can be estimated. Moreover, we confirm numerically the stability criterion which was earlier found following a von Neumann analysis. Finally, the `motion' of the wave-function due to the underlying discreteness of the space-time is investigated, for both a constant lattice, as well as lattice refinement models.
dc.description17 pages, 14 figures
dc.identifierhttps://arxiv.org/abs/0803.4483
dc.identifierhttp://arxiv.org/abs/0803.4483
dc.identifierPhys.Rev.D78:024030,2008
dc.identifierdoi:10.1103/PhysRevD.78.024030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/211161
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectAstrophysics
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titleNumerical techniques for solving the quantum constraint equation of generic lattice-refined models in loop quantum cosmology
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