Density spectra for knots

We recently discovered a relationship between the volume density spectrum and the determinant density spectrum for infinite sequences of hyperbolic knots. Here, we extend this study to new quantum density spectra associated to quantum invariants, such as Jones polynomials, Kashaev invariants and knot homology. We also propose related conjectures motivated by geometrically and diagrammatically maximal sequences of knots.
Comment: 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:1411.7915. substantial text overlap with arXiv:1411.7915