Vibrational mechanics in higher dimension: Tuning potential landscapes

Mirror Manifolds in Higher Dimension

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and hence naturally generalize to other dimensions. The moduli spaces for Calabi–Yau d-folds are somewhat different from the “special Kähler manifolds” which had...

Gravitational Collapse in Higher Dimension

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional spacetime and appearance of naked singularity has been analyzed both for non-marginal and marginally bound cases. It has been shown that naked singularity is possible for any arbitrary dimension in non-marginally bound case. For marginally bound case we have examined the radial null geodesics from the singu...

Convexity Ranks in Higher Dimension

Vibrational mechanics in an optical lattice: controlling transport via potential renormalization.

We demonstrate theoretically and experimentally the phenomenon of vibrational resonance in a periodic potential, using cold atoms in an optical lattice as a model system. A high-frequency (HF) drive, with a frequency much larger than any characteristic frequency of the system, is applied by phase modulating one of the lattice beams. We show that the HF drive leads to the renormalization of the ...

Valiron’s Construction in Higher Dimension

We consider holomorphic self-maps φ of the unit ball B in C (N = 1, 2, 3, ...). In the one-dimensional case, when φ has no fixed points in D := B and is of hyperbolic type, there is a classical renormalization procedure due to Valiron which allows to semi-linearize the map φ, and therefore, in this case, the dynamical properties of φ are well understood. In what follows, we generalize the class...