Niall D. Whelan

Learn More
We develop sampling algorithms for multivariate Archimedean copulas. For exchangeable copulas, where there is only one generating function, we first analyse the distribution of the copula itself, deriving a number of integral representations and a generating function representation. One of the integral representations is related, by a form of convolution,(More)
We study the effect on quantum spectra of the existence of small circular disks in a billiard system. In the limit where the disk radii vanish there is no effect, however this limit is approached very slowly so that even very small radii have comparatively large effects. We include diffractive orbits which scatter off the small disks in the periodic orbit(More)
Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in the classical mechanics. An important example is a billiard with sharp corners; its semiclassical quantisation requires the inclusion of diffractive periodic orbits in addition to classical periodic orbits. In this paper we(More)
We discuss the symmetry decomposition of the average density of states for the two dimensional potential V = x2y2 and its three dimensional generalisation V = x2y2 + y2z2 + z2x2. In both problems, the energetically accessible phase space is non-compact due to the existence of infinite channels along the axes. It is known that in two dimensions the phase(More)
We consider the extension of the Gutzwiller trace formula to systems of two or more identical particles. We first study the case of two noninteracting particles. Important considerations are the structure of the periodic orbits, which come in families and the symmetry decomposition of the density of states. Interactions cause the periodic orbit families to(More)
Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated with a symmetry which the classical Hamiltonian does not share. A local analysis in the vicinity of these special tori(More)