2012/12/31 by Christopher E. Coleman-Smith, C. E. Coleman-Smith, Berndt Müller +1 · 5 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Chaotic #Classical mechanics #Cosmology and Gravitation Theories #Geometry #Hamiltonian (control theory) #Hamiltonian system #Instability #Lyapunov exponent #Mathematics #Noncommutative and Quantum Gravity Theories #Nonlinear system #Phase space #Physics #Polyhedron #Quantum mechanics #Statistical physics #gr-qc #hep-th #nlin.CD
paper · pdf · doi:10.1103/physrevd.87.044047
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 87(4) (American Physical Society) · 20 Pages, 19 Figures. Updated to submitted version, minor edits
arxiv created 2013/01/06 · openalex publication_date 2013/02/21 · arxiv updated 2013/03/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present an analysis of the dynamics of the equifacial pentahedron on the Kapovich-Millson phase space under a volume preserving Hamiltonian. The classical dynamics of polyhedra under such a Hamiltonian may arise from the classical limit of the node volume operators in loop quantum gravity. The pentahedron is the simplest nontrivial polyhedron for which the dynamics may be chaotic. We consider the distribution of polyhedral configurations throughout the space and find indications that the borders between certain configurations act as separatrices. We examine the local stability of trajectories within this phase space and find that locally unstable regions dominate although extended stable regions are present. Canonical and microcanonical estimates of the Kolmogorov-Sinai entropy suggest that the pentahedron is a strongly chaotic system. The presence of chaos is further suggested by calculations of intermediate time Lyapunov exponents which saturate to nonzero values.